Absolutely summing operators:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
1995
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
43 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 474 S. |
| ISBN: | 0521431689 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV010491661 | ||
| 003 | DE-604 | ||
| 005 | 20190625 | ||
| 007 | t | ||
| 008 | 951123s1995 |||| 00||| eng d | ||
| 020 | |a 0521431689 |9 0-521-43168-9 | ||
| 035 | |a (OCoLC)32166449 | ||
| 035 | |a (DE-599)BVBBV010491661 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-91G |a DE-824 |a DE-12 |a DE-703 |a DE-19 |a DE-11 |a DE-188 | ||
| 050 | 0 | |a QA329.2 | |
| 082 | 0 | |a 515/.7246 |2 20 | |
| 084 | |a SK 620 |0 (DE-625)143249: |2 rvk | ||
| 084 | |a SK 600 |0 (DE-625)143248: |2 rvk | ||
| 084 | |a MAT 470f |2 stub | ||
| 100 | 1 | |a Diestel, Joseph |d 1943- |e Verfasser |0 (DE-588)108479773 |4 aut | |
| 245 | 1 | 0 | |a Absolutely summing operators |c Joe Diestel ; Hans Jarchow ; Andrew Tonge |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1995 | |
| 300 | |a XV, 474 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 43 | |
| 650 | 7 | |a Banachruimten |2 gtt | |
| 650 | 7 | |a Functionaalanalyse |2 gtt | |
| 650 | 7 | |a Operatoren |2 gtt | |
| 650 | 7 | |a Opérateurs linéaires |2 ram | |
| 650 | 4 | |a Absolutely summing operators | |
| 650 | 0 | 7 | |a p-Summierbarkeit |0 (DE-588)4176174-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Banach-Raum |0 (DE-588)4004402-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operator |0 (DE-588)4130529-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Banach-Raum |0 (DE-588)4004402-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Operator |0 (DE-588)4130529-2 |D s |
| 689 | 1 | 1 | |a p-Summierbarkeit |0 (DE-588)4176174-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Jarchow, Hans |e Verfasser |4 aut | |
| 700 | 1 | |a Tonge, Andrew |e Verfasser |4 aut | |
| 830 | 0 | |a Cambridge studies in advanced mathematics |v 43 |w (DE-604)BV000003678 |9 43 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-006990794 | ||
Datensatz im Suchindex
| _version_ | 1804124924293414912 |
|---|---|
| adam_text | IMAGE 1
ABSOLUTELY SUMMING
OPERATORS
JOE DIESTEL
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE KENT STATE UNIVERSITY
HANS JARCHOW MATHEMATISCHES INSTITUT UNIVERSITAT ZURICH
ANDREW TONGE
DEPARTMENT OF MATHEMATICS AND COMPUTER SCIENCE KENT STATE UNIVERSITY
CAMBRIDGE UNIVERSITY PRESS
IMAGE 2
CONTENTS
INTRODUCTION XI
NOTATION XIII
1. UNCONDITIONAL AND ABSOLUTE SUMMABILITY IN BANACH SPACES 1 THE
DVORETZKY - ROGERS THEOREM I
ABSOLUTELY CONVERGENT SERIES ARE UNCONDITIONALLY CONVERGENT IN BANACH
SPACES, DVORETZKY-ROGERS THEOREM, COINCIDENCE OF ABSOLUTE AND
UNCONDITIONAL SUMMA- BILITY ONLY IN FINITE DIMENSIONAL SPACES
UNCONDITIONAL CONVERGENCE AND THE ORLICZ - PETTIS THEOREM 4 SIMPLE
CHARACTERIZATIONS OF UNCONDITIONAL SUMMABILITY, BOUNDED MULTIPLIER TEST,
SCHUR S LI THEOREM, ORLICZ - PETTIS THEOREM, OMNIBUS THEOREM ON
UNCONDITIONAL SUMMABILITY KHINCHIN S INEQUALITY 9
RADEMACHER FUNCTIONS, KHINCHIN S INEQUALITY, ORLICZ S THEOREM ON
UNCONDITIONAL SUMMABILITY IN LI, SPAN OF THE RADEMACHER FUNCTIONS IN L
P[O,1]
GROTHENDIECK S INEQUALITY 15
ABSOLUTELY SUMMING OPERATORS, GROTHENDIECK S THEOREM ON OPERATORS FROMI
TO 2, GROTHENDIECK S INEQUALITY, GROTHENDIECK S THEOREM ON FINITE
DIMENSIONAL SPACES NOTES AND REMARKS 19
2. FUNDAMENTALS OF P-SUMMING OPERATORS 31
DEFINITION 31
P-SUMMING OPERATORS, P-SUMMING NORM V E C T O R - V A L U ED S E Q U E N
CE S P A C ES , 32
STRONG L P SEQUENCES, WEAK LP SEQUENCES, CHARACTERIZATION OF P-SUMMING
OPERATORS
C O N S T R U C T I O NS OF P - S U M M I NG O P E R A T O RS 36
FINITE RANK OPERATORS, THE BANACH IDEAL OF P-SUMMING OPERATORS,
INJECTIVITY, INCLUSION THEOREM B A S IC E X A M P L ES ,40
MULTIPLICATION OPERATORS, FORMAL INCLUSION OPERATORS, DIAGONAL
OPERATORS,
EMBEDDINGS OF FUNCTION SPACES, KERNEL OPERATORS D O M I N A T I ON AND
FACTORIZATION 43
PIETSCH DOMINATION THEOREM, PIETSCH FACTORIZATION THEOREM, OPERATORS
FROM AND TO C(K )-SPACES, 2-SUMMING OPERATORS S O ME C O N S E Q U E N C
ES 49
WEAK COMPACTNESS AND COMPLETE CONTINUITY OF P-SUMMING OPERATORS, WEAK
DVORETZKY - ROGERS THEOREM, P-SUMMING CHARACTER OF BIADJOINTS AND
ADJOINTS C O M P O S I T I ON 52
N O T ES AND R E M A R KS 55
3. SUMMING OPERATORS ON P -SPACES 60
P-SPACES 60
OPERATORS FROM I-SPACES TO 2-SPACES ARE 1-SUMMING, APPROXIMATION IN L
P(II) AND C(K), LP(JI) AND C(K) AS BASIC EXAMPLES OF P-SPACES
O P E R A T O RS ON O O - S P A C ES 64
OPERATORS FROM COO -SPACES TO P-SPACES (L P 2) ARE 2-SUMMING S O ME A
P P L I C A T I O NS , 66
QUOTIENTS OF C{K) WHICH ARE SUBSPACES OF 1, COINCIDENCE OF 2-SUMMING
AND 1-SUM- MING OPERATORS ON SUBSPACES OF P (L P 2), UNIQUENESS OF
UNCONDITIONAL BASIS IN TI,
IMAGE 3
VI CONTENTS
LI[O,L] HAS NO UNCONDITIONAL BASIS, COINCIDENCE OF G-SUMMING AND
2-SUMMING OPERATORS ON SUBSPACES OF C P FOR L P 2 Q OO, EXTRAPOLATION
THEOREM
NOTES AND REMARKS 73
4. OPERATORS ON HILBERT SPACES AND S U M M I NG OPERATORS 76
COMPACT HILBERT SPACE OPERATORS 76
SPECTRAL THEOREM, ORTHONORMAL REPRESENTATION, APPROXIMATION NUMBERS
SCHATTEN-VON NEUMANN CLASSES 80
GENERAL THEORY, HILBERT - SCHMIDT OPERATORS HILBERT-SCHMIDT OPERATORS
AND SUMMING OPERATORS 84 COINCIDENCE WITH 2-SUMMING OPERATORS, WITH
P-SUMMING OPERATORS, CHARACTERIZATION BY FACTORIZATION
E X T E N S I ON P R O P E R TY 85
INJECTIVE BANACH SPACES, N 2-EXTENSION THEOREM, KADETS - SNOBAR THEOREM
ADJOINTS OF 2-SUMMING OPERATORS 88
NOTES AND REMARKS 90
5. P-INTEGRAL OPERATORS 95
DEFINITION AND ELEMENTARY PROPERTIES 95
P-INTEGRAL OPERATORS, BANACH IDEAL PROPERTY, STRICTLY P-INTEGRAL
OPERATORS R E L A T I O NS TO P- S U M M I NG O P E R A T O RS 97
P-INTEGRAL OPERATORS ARE P-SUMMING, CONDITIONS FOR THE CONVERSE, FURTHER
CASES OF COINCIDENCE
P - S U M M I NG O P E R A T O RS FAILING TO BE P - I N T E G R AL 99
F U R T H ER S T R U C T U R AL R E S U L TS 104
P-INTEGRALITY OF SECOND ADJOINTS, THE CASE P=L, COMPOSITION OF SUMMING
AND INTEGRAL OPERATORS
O R D ER B O U N D E D N E SS 107
DEFINITIONS, L P(/I)-VALUED ORDER BOUNDED OPERATORS ARE P-INTEGRAL,
CONVERSE FOR P=L, OPERATORS WITH P-SUMMING ADJOINT
P - N U C L E AR O P E R A T O RS 111
VARIOUS CHARACTERIZATIONS OF P-NUCLEAR OPERATORS, BANACH IDEAL PROPERTY
R E L A T I O NS TO I N T E G R AL O P E R A T O RS 114
P-NUCLEAR OPERATORS ARE P-INTEGRAL, CASES OF COINCIDENCE, FACTORIZATION,
COMPOSITION OF SUMMING AND NUCLEAR OPERATORS
HILBERT SPACE OPERATORS US
P-NUCLEAR AND P-INTEGRAL OPERATORS ON HILBERT SPACE, COMPOSITION OF
2-SUMMING OPERATORS
NOTES AND REMARKS 119
6. TRACE DUALITY 125
T R A CE 125
TRACE AND TRACE DUALITY IN FINITE DIMENSIONS D U A L I TY F OR S C H A T
T EN - V ON N E U M A NN C L A S S ES 126
COMPOSITION THEOREM, TRACE AND DUALITY FOR SCHATTEN-VON NEUMANN CLASSES
B A N A CH I D E A LS 130
OPERATOR IDEALS AND THEIR NORMS, BANACH IDEALS, COMPARISON
A D J O I NT I D E A LS 132
ADJOINT IDEALS, BIADJOINT CRITERION
M A X I M AL I D E A LS 134
ORDERING BANACH IDEALS, MAXIMALITY, MAXIMALITY AND ADJOINTS, MAXIMALITY
OF P-INTEGRAL OPERATORS, ADJOINTS OF P-INTEGRAL OPERATORS, MAXIMALITY OF
G-SUMMING OPERATORS, MINIMALITY OF P-NUCLEAR OPERATORS, CHARACTERIZATION
OF TO-SPACES
IMAGE 4
CONTENTS VII
A P P L I C A T I O NS 143
LEWIS THEOREM, AUERBACH S LEMMA, JOHN S ELLIPSOIDS, CARATHEODORY S
THEOREM
N O T ES AND R E M A R KS 151
7. 2-FACTORABLE OPERATORS 154
G E N E R A L I T I ES 154
THE BANACH IDEAL OF P-FACTORABLE OPERATORS, ADJOINTS, THE CASE P=2 M A X
I M A L I TY OF [F 2,72] 156
R E L A T I O NS W I TH G R O T H E N D I E C K S I N E Q U A L I TY .
157
MATRICIAL CHARACTERIZATION, PREPARATIONS FOR MAUREY S EXTENSION THEOREM
2 - D O M I N A T ED O P E R A T O RS 162
DEFINITION, MAXIMALITY, TRACE DUALITY OF 2-DOMINATED AND 2-FACTORABLE
OPERATORS, FURTHER CHARACTERIZATIONS N O T ES A ND R E M A R KS 166
8. ULTRAPRODUCTS AND LOCAL REFLEXIVITY 169
G E N E R A L I T I ES ON U L T R A P R O D U C TS 169
ULTRAPRODUCT OF BANACH SPACES AND OPERATORS, ULTRAPOWERS, ULTRAPRODUCTS
OF FINITE DIMENSIONAL SPACES S O ME S T A B I L I TY P R O P E R T I ES
172
BANACH LATTICES, L P (FT)-SPACES, C(K)-SPACES, BANACH ALGEBRAS AND
ULTRAPRODUCTS U L T R A P R O D U C TS A ND F I N I TE D I M E N S I O N
AL S T R U C T U RE 173
BANACH SPACES AS SUBSPACES OF ULTRAPRODUCTS OF FINITE DIMENSIONAL
SUBSPACES, REPRESENTATION OF OPERATORS BY ULTRAPRODUCTS OF FINITE
DIMENSIONAL OPERATORS F I N I TE R E P R E S E N T A B I L I TY 175
CONCEPTS, RELATION WITH ULTRAPRODUCTS, APPLICATION TO L P (FI)- AND
C(JF)-SPACES L O C AL R E F L E X I V I TY 177
HELLY S LEMMA, PRINCIPLE OF LOCAL REFLEXIVITY, APPLICATION TO BIDUALS
N O T ES A ND R E M A R KS 182
9. P-FACTORABLE OPERATORS 185
M A X I M A L I TY OF T P I85
MAXIMALITY, INCLUSIONS
D U AL IDEALS , 186
DEFINITION, ADJOINTS AND MAXIMALITY OF DUAL IDEALS
^ - D O M I N A T ED O P E R A T O RS 187
DEFINITION AND CHARACTERIZATIONS, MAXIMALITY, TRACE DUALITY OF
P-FACTORABLE AND P*-DOMINATED OPERATORS P R O OF OF T HE M A IN R E S U
LT 190
KY FAN S LEMMA A P P L I C A T I O NS 192
CHARACTERIZATION OF COMPLEMENTED SUBSPACES, SUBSPACES AND QUOTIENTS OF L
P (/I)-SPACES, EXTENSIONS OF P-FACTORABLE OPERATORS N O T ES AND R E M A
R KS .. 195
10. ( 7,P)-SUMMING OPERATORS 197
SOME BASIC PROPERTIES ^ 197
FUNDAMENTALS, BANACH IDEAL PROPERTY, (Q,2)-SUMMING OPERATORS AND
SCHATTEN - VON NEUMANN CLASSES, INCLUSION THEOREM, DVORETZKY - ROGERS
THEOREM O P E R A T O RS ON O O - S P A C ES 199
OPERATORS FROM *, TO P , P 2, RESULTS OF INTERPOLATION AND
FACTORIZATION FOR (Q,P)-SUMMING OPERATORS ON C(IF)-SPACES, COINCIDENCE
OF (G,L)-SUMMING AND (G,P)-SUMMING OPERATORS ON C(K)-SPACES (Q P),
APPLICATIONS N O T ES AND R E M A R KS 207
IMAGE 5
VIII CONTENTS
11. TYPE AND COTYPE: THE BASICS 211
KAHANE S INEQUALITY R A N D O M I Z ED S U MS 212
FUNDAMENTALS, LEVY S INEQUALITY
RADEMACHER SUMS 214
RADEMACHER SUMS IN R 216
PROOF OF KAHANE S INEQUALITY T Y PE AND C O T Y PE 217
DEFINITIONS, TYPE AND COTYPE OF R-SPACES, PERMANENCE PROPERTIES, TYPE
AND COTYPE OF LEBESGUE - BOCHNER SPACES SUMMING OPERATORS 222
COTYPE AND INCLUSION THEOREMS FOR SUMMING OPERATORS, COTYPE AND SUMMING
OPERATORS ON C(K )-SPACES, ORLICZ S THEOREM AND COTYPE, SUBSPACES OF LX
HAVING TYPE 1 N O T ES AND REMARKS 225
1 2. RANDOMIZED SERIES AND ALMOST SUMMING OPERATORS 230
RANDOMIZED SERIES 230
ALMOST SURE SUMMABILITY, STANDARD CHARACTERIZATIONS
R A D E M A C H ER S E R I ES 231
CONTRACTION PRINCIPLE, ALMOST SURE SUMMABILITY AND CONVERGENCE IN L
P(X), THE BANACH SPACE RAD(X), RELATIONS TO TYPE AND COTYPE A L M O ST S
U M M I NG O P E R A T O RS 234
DEFINITION, P-SUMMING OPERATORS ARE ALMOST SUMMING, ALMOST SUMMING
OPERATORS AND COTYPE, IDEAL PROPERTIES OF ALMOST SUMMING OPERATORS, TYPE
2 AND ALMOST SUMMING OPERATORS GAUSSIAN VARIABLES 237
APPLICATIONS TO A L M O ST SUMMING OPERATORS 239
CHARACTERIZATION OF ALMOST SUMMING OPERATORS USING GAUSSIAN VARIABLES,
THE Y-SUMMING NORM, 2-DOMINATED AND ALMOST SUMMING OPERATORS S O ME C O
N S E Q U E N C ES 246
KWAPIERI S THEOREM, MAUREY S EXTENSION THEOREM, APPLICATIONS
GAUSSIAN T Y PE AND C O T Y PE 248
DEFINITIONS, RELATIONS TO TYPE AND COTYPE
T HE M A U R EY - R O S E N T H AL T H E O R EM 251
STATEMENT OF THE THEOREM, A DILATION THEOREM, BENNETT - MAUREY - NAHOUM
DECOM- POSITION OF UNCONDITIONALLY SUMMABLE SEQUENCES IN LI N O T ES AND
R E M A R KS 255
13. K-CONVEXITY AND B-CONVEXITY 258
K-CONVEXITY 259
DEFINITIONS, UNIFORM CONTAINMENT OF ! S B-CONVEXITY 261
FUNDAMENTALS, CHARACTERIZATION BY UNIFORM CONTAINMENT OF ^ S,
B-CONVEXITY AND DUALITY, B-CONVEXITY AND TYPE EQUIVALENCE OF B- AND K -
C O N V E X I TY 267
SEMIGROUPS OF OPERATORS, BEURLING - KATO THEOREM, PROOF OF THE MAIN
THEOREM
S O ME C O N S E Q U E N C ES 275
DUALITY BETWEEN TYPE AND COTYPE IN K-CONVEX SPACES, REFLEXIVE SUBSPACES
OF L
N O T ES AND REMARKS 280
IMAGE 6
CONTENTS IX
14. SPACES WITH FINITE COTYPE 283
FINITE COTYPE IS EQUIVALENT TO NON-UNIFORM CONTAINMENT OF 12O S D V O R
E T Z KY - R O G E RS A G A IN 283
F A C T O R I NG F O R M AL I D E N T I T I ES . -.. 286
T HE M A IN T H E O R EM 289
COTYPE VERSUS FINITE FACTORIZATION AND ORLICZ S THEOREM, COTYPE NUMBERS,
COTYPE NUMBERS OF LEBESGUE- BOCHNER SPACES, PROOFS B R U N E L - S U C H
E S T ON A F F A I RS 298
RAMSEY S THEOREM, BRUNEL-SUCHESTON THEOREM, INVARIANCE UNDER SPREADING
N O T ES AND R E M A R KS 303
1 5. WEAKLY COMPACT OPERATORS ON C(IF)-SPACES 309
CHARACTERIZATION OF WEAKLY COMPACT OPERATORS 309 AN A P P R O X I M A T
I ON S C H E ME 311
APPROXIMATION BY P-SUMMING OPERATORS, CHARACTERIZATIONS AND PROPERTIES
U L T R A P O W ER S T A B I L I TY 313
PROPERTY (H), TYPE AND COTYPE, ROSENTHAL S THEOREM ON REFLEXIVE
SUBSPACES OF LI
S P A C ES V E R I F Y I NG G R O T H E N D I E C K S T H E O R EM 316
SUBSPACES OF C(K) LEADING TO REFLEXIVE QUOTIENTS, KISLIAKOV S LEMMA,
FINITE COTYPE IS A THREE SPACE PROPERTY, GROTHENDIECK S THEOREM FOR
QUOTIENTS OF L BY A REFLEXIVE SUBSPACE N O T ES AND REMARKS 318
16. T Y PE AND C O T Y PE IN B A N A CH LATTICES 326
F U N C T I O N AL C A L C U L US 326
ABSTRACT M-SPACES, KAKUTANI S REPRESENTATION THEOREM, KHINCHIN S
INEQUALITY IN BANACH LATTICES, COMPLEXIFICATION OF A BANACH LATTICES (
? , P ) - C O N C A VE O P E R A T O RS 330
DEFINITION, CHARACTERIZATION VIA (G,L)-SUMMING OPERATORS, COTYPE OF A
BANACH LATTICE, MAUREY-KHINCHIN INEQUALITY T HE R O LE OF D I S J O I N
T N E SS 333
(G,L)-SUMMING OPERATORS ON C(K) VIA DISJOINTLY SUPPORTED FUNCTIONS,
COTYPE Q (2 Q OO) OF A BANACH LATTICE IS DETERMINED ON DISJOINT VECTORS,
MAUREY - KHINCHIN INEQUALITY AND FINITE COTYPE, ORDER BOUNDED AND ALMOST
SUMMING OPERATORS T Y PE AND C O N V E X I TY 340
(P,Q)-CONVEX OPERATORS, DUALITY WITH (P*,G*)-CONCAVITY, TYPE OF BANACH
LATTICES
N O T ES AND R E M A R KS 341
17. LOCAL UNCONDITIONALITY 344
UNCONDITIONAL BASIS, UNCONDITIONAL BASIS CONSTANT L O C AL U N C O N D I
T I O N AL S T R U C T U RE J 344
DEFINITIONS, BANACH LATTICES HAVE L.U.ST., X HAS L.U.ST. IFF X IS
COMPLEMENTED IN A BANACH LATTICE, L.U.ST. AND DUALITY T HE G O R D ON -
L E W IS I N E Q U A L I TY 349
G L - S P A C ES 350
DEFINITIONS AND DUALITY
G L - S P A C ES A ND C O T Y PE 352
GL-SPACES OF COTYPE 2, DUALITY OF TYPE AND COTYPE IN GL-SPACES
A(2)-SETS 355
IMAGE 7
X CONTENTS
BANACH SPACES FAILING (GL) 358
FAILURE OF (GL) IN (^2) AND IN SCHATTEN-VON NEUMANNN CLASSES S P , P^2
NOTES AND REMARKS 363
18. SUMMING ALGEBRAS 373
P-SUMMING ALGEBRAS 373
DEFINITIONS, ELEMENTARY PROPERTIES AND EXAMPLES P O L Y N O M I AL I N E
Q U A L I T I ES 375
POLYNOMIALS, NORMS OF POLYNOMIALS, SYMMETRIC MULTILINEAR FORMS,
QUOTIENTS OF P-SUMMING ALGEBRAS Q-ALGEBRAS AND OPERATOR ALGEBRAS 378
Q-ALGEBRAS AND QUOTIENTS OF 1-SUMMING ALGEBRAS, QUOTIENT ALGEBRAS OF
UNIFORM ALGEBRAS ARE OPERATOR ALGEBRAS A COMMUTATIVE N O N - O P E R A T
OR ALGEBRA 38I
THE WIENER ALGEBRA IS NOT AN OPERATOR ALGEBRA
FAILURE OF THE MANY VARIABLE VON NEUMANN INEQUALITY 383 A COMMUTATIVE N
O N -Q OPERATOR ALGEBRA 386
2-SUMMING ALGEBRAS AND OPERATOR ALGEBRAS 387
2-SUMMING ALGEBRAS ARE OPERATOR ALGEBRAS STRICTLY P-SUMMING ALGEBRAS 390
STRICTLY P-SUMMING ALGEBRAS ARE UNIFORM ALGEBRAS NOTES AND REMARKS 393
19. DVORETZKY S THEOREM AND FACTORIZATION OF OPERATORS 396 DVORETZKY S
THEOREM, FACTORIZING HILBERT - SCHMIDT OPERATORS, CHARACTERIZATION OF
K-CONVEXITY
F R E C H ET DERIVATIVES OF CONVEX FUNCTIONS 397
G R O UP ACTIONS AND INVARIANT MEASURES 400
ACTIONS OF THE ORTHOGONAL G R O UP 403
ACTION ON SPHERES, ON GRASSMANNIANS P R O OF OF D V O R E T Z K Y S T H
E O R EM 406
DVORETZKY - ROGERS NORMS, PROOF OF THE THEOREM, COTYPE OF SPACES OF
COMPACT OPERATORS, TYPE OF SPACES OF NUCLEAR OPERATORS B A S IC S E Q U
E N C ES 410
SPECIAL BLOCKING OF BASIC SEQUENCES
FACTORIZATION 412
FACTORIZATION OF COMPACT HILBERT SPACE OPERATORS THROUGH SUBSPACES OF
ARBITRARY BANACH SPACES, APPLICATION TO HILBERT - SCHMIDT OPERATORS,
GENERALIZATIONS C O M P L E M E N T A T I ON 416
COTYPE 2 NUMBERS AND 7-SUMMING NORM, EXISTENCE OF FINITE RANK
PROJECTIONS OF NICE NORMS K - C O N V E X I TY 420
GEODESIC METRIC, ISOPERIMETRIC INEQUALITY, LEVY S LEMMA, X IS K-CONVEX
IFF IT CONTAINS THE % S UNIFORMLY AND UNIFORMLY COMPLEMENTED T HE I S
O P E R I M E T R IC I N E Q U A L I TY 424
CAPS, QUALITATIVE VERSION OF THE ISOPERIMETRIC INEQUALITY, BLASCHKE S
SELECTION THEOREM, SPHERICAL SYMMETRIZATION
N O T ES AND R E M A R KS 431
REFERENCES 435
AUTHOR INDEX 465
SUBJECT INDEX 469
|
| any_adam_object | 1 |
| author | Diestel, Joseph 1943- Jarchow, Hans Tonge, Andrew |
| author_GND | (DE-588)108479773 |
| author_facet | Diestel, Joseph 1943- Jarchow, Hans Tonge, Andrew |
| author_role | aut aut aut |
| author_sort | Diestel, Joseph 1943- |
| author_variant | j d jd h j hj a t at |
| building | Verbundindex |
| bvnumber | BV010491661 |
| callnumber-first | Q - Science |
| callnumber-label | QA329 |
| callnumber-raw | QA329.2 |
| callnumber-search | QA329.2 |
| callnumber-sort | QA 3329.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 620 SK 600 |
| classification_tum | MAT 470f |
| ctrlnum | (OCoLC)32166449 (DE-599)BVBBV010491661 |
| dewey-full | 515/.7246 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7246 |
| dewey-search | 515/.7246 |
| dewey-sort | 3515 47246 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02073nam a2200541 cb4500</leader><controlfield tag="001">BV010491661</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20190625 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">951123s1995 |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0521431689</subfield><subfield code="9">0-521-43168-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)32166449</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV010491661</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-355</subfield><subfield code="a">DE-91G</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-188</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA329.2</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">515/.7246</subfield><subfield code="2">20</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 620</subfield><subfield code="0">(DE-625)143249:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 600</subfield><subfield code="0">(DE-625)143248:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 470f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Diestel, Joseph</subfield><subfield code="d">1943-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)108479773</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Absolutely summing operators</subfield><subfield code="c">Joe Diestel ; Hans Jarchow ; Andrew Tonge</subfield></datafield><datafield tag="250" ind1=" " ind2=" "><subfield code="a">1. publ.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Cambridge [u.a.]</subfield><subfield code="b">Cambridge Univ. Press</subfield><subfield code="c">1995</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XV, 474 S.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">43</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Banachruimten</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Functionaalanalyse</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Operatoren</subfield><subfield code="2">gtt</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Opérateurs linéaires</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Absolutely summing operators</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">p-Summierbarkeit</subfield><subfield code="0">(DE-588)4176174-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Operator</subfield><subfield code="0">(DE-588)4130529-2</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Banach-Raum</subfield><subfield code="0">(DE-588)4004402-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Operator</subfield><subfield code="0">(DE-588)4130529-2</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">p-Summierbarkeit</subfield><subfield code="0">(DE-588)4176174-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Jarchow, Hans</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tonge, Andrew</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Cambridge studies in advanced mathematics</subfield><subfield code="v">43</subfield><subfield code="w">(DE-604)BV000003678</subfield><subfield code="9">43</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-006990794</subfield></datafield></record></collection> |
| id | DE-604.BV010491661 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T17:53:23Z |
| institution | BVB |
| isbn | 0521431689 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006990794 |
| oclc_num | 32166449 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-12 DE-703 DE-19 DE-BY-UBM DE-11 DE-188 |
| owner_facet | DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-824 DE-12 DE-703 DE-19 DE-BY-UBM DE-11 DE-188 |
| physical | XV, 474 S. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Diestel, Joseph 1943- Verfasser (DE-588)108479773 aut Absolutely summing operators Joe Diestel ; Hans Jarchow ; Andrew Tonge 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1995 XV, 474 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 43 Banachruimten gtt Functionaalanalyse gtt Operatoren gtt Opérateurs linéaires ram Absolutely summing operators p-Summierbarkeit (DE-588)4176174-1 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s DE-604 Operator (DE-588)4130529-2 s p-Summierbarkeit (DE-588)4176174-1 s Jarchow, Hans Verfasser aut Tonge, Andrew Verfasser aut Cambridge studies in advanced mathematics 43 (DE-604)BV000003678 43 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diestel, Joseph 1943- Jarchow, Hans Tonge, Andrew Absolutely summing operators Cambridge studies in advanced mathematics Banachruimten gtt Functionaalanalyse gtt Operatoren gtt Opérateurs linéaires ram Absolutely summing operators p-Summierbarkeit (DE-588)4176174-1 gnd Banach-Raum (DE-588)4004402-6 gnd Operator (DE-588)4130529-2 gnd |
| subject_GND | (DE-588)4176174-1 (DE-588)4004402-6 (DE-588)4130529-2 |
| title | Absolutely summing operators |
| title_auth | Absolutely summing operators |
| title_exact_search | Absolutely summing operators |
| title_full | Absolutely summing operators Joe Diestel ; Hans Jarchow ; Andrew Tonge |
| title_fullStr | Absolutely summing operators Joe Diestel ; Hans Jarchow ; Andrew Tonge |
| title_full_unstemmed | Absolutely summing operators Joe Diestel ; Hans Jarchow ; Andrew Tonge |
| title_short | Absolutely summing operators |
| title_sort | absolutely summing operators |
| topic | Banachruimten gtt Functionaalanalyse gtt Operatoren gtt Opérateurs linéaires ram Absolutely summing operators p-Summierbarkeit (DE-588)4176174-1 gnd Banach-Raum (DE-588)4004402-6 gnd Operator (DE-588)4130529-2 gnd |
| topic_facet | Banachruimten Functionaalanalyse Operatoren Opérateurs linéaires Absolutely summing operators p-Summierbarkeit Banach-Raum Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006990794&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT diesteljoseph absolutelysummingoperators AT jarchowhans absolutelysummingoperators AT tongeandrew absolutelysummingoperators |