Weakly compact sets: lectures held at S.U.N.Y., Buffalo, in Spring 1978
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
1980
|
| Schriftenreihe: | Lecture notes in mathematics
801 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 123 S. |
| ISBN: | 3540099913 0387099913 |
Internformat
MARC
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| 100 | 1 | |a Floret, Klaus |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Weakly compact sets |b lectures held at S.U.N.Y., Buffalo, in Spring 1978 |c Klaus Floret |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1980 | |
| 300 | |a VII, 123 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 801 | |
| 650 | 4 | |a Espaces compacts | |
| 650 | 4 | |a Espaces localement convexes | |
| 650 | 4 | |a Espaces vectoriels topologiques | |
| 650 | 4 | |a Compact spaces | |
| 650 | 4 | |a Linear topological spaces | |
| 650 | 4 | |a Locally convex spaces | |
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Datensatz im Suchindex
| _version_ | 1804116719027879936 |
|---|---|
| adam_text | CONTENTS
§0 Some fundamentals of locally convex spaces 1
0.2. Weak topology, dual systems; 0.3. Mackey-topology;
0.4. Barrels, barrel-lemma, bounded sets; 0.5. Strong topology,
semi-reflexive spaces; 0.6. Grothendieck s completeness
criterion; 0.7. Extreme points; 0.8. (LF)-spaces.
§1 Countably compact sets and the theorem of Eberlein-Grothendieck.... 7
1.1. Definition of countably and sequentially compact sets;
1.2. Basic properties and counter-examples; 1.4. The inter¬
changeable double-limit-property, pointwise convergence and
relatively compact sets in C(X,Z); 1.5. Pointwise compact¬
ness in C(X) and C-^(X) ; 1.6. Weak countable compactness in
locally convex spaces: Eberlein-Grothendieck theorem;
1.8. Other locally convex topologies
Exercises: 1.15. A criterion of V. L. Smulian; 1.22. Another
approach to the Eberlein-Grothendieck theorem.
§2 Bounding sets in the weak topology 21
2.1. Bounding and pseudocompact sets, the Tychonoff-Plank;
2.3. Weakly bounding = weakly relatively compact; 2.5. Weakly
pseudocompact = weakly relatively compact; 2.7. Other locally
convex topologies.
Exercises
§3 Sequential compactness and angelic spaces 28
3.1. The angelic-lemma; 3.2. Smulian1s theorem for locally
convex spaces with weakly separable dual; 3.3. Angelic spaces,
the basic theorem; 3.5. Fremlin s result; 3.6. Some sets with
closure = sequential closure (DeWilde); 3.7. C(X,Z) being
pointwise angelic; 3.8. and 3.9. The Kaplansky result on
closures; 3.10. Weakly angelic locally convex spaces: Eberlein-
Smulian theorem
Exercises: 3.17. Products of angelic spaces; 3.20. Another
approach to pointwise angelic spaces C(X,Z); 3.27. Weakly
integrable, vector-valued functions.
VI
§4 Pointwise and weak compactness in spaces of continuous functions.. 45
4.1. Compact-open and bounding-open topology; 4.2. Compactness
in C(K) - Grothendieck s theorem; 4.3. In CCO(X); 4.4. In
C*(X); 4.5. The repletion; 4.7. Bounding sets in uX; 4.8. In
CWg(X); 4.9. Convex sets.
Exercises: 4.11. Locally compact X; 4.24. Measurable
functions; 4.25. Cauchy-sequences.
§5 Best approximations and the theorem of R.C. James 57
5.1. Mazur s observation; 5.2. Best-approximation; 5.3. The
evolution to James1 theorem; 5.4. The reflexivity-criterion;
5.5. Sequences of convex sets (Dieudonne-Smulian theorem) and
proximinal sets; 5.6. James theorem does not hold in normed
spaces.
Exercises: 5.17. and 5.19. More characterisations of weakly
compact sets.
§6 Proof of the theorem of R.C. James 67
6.2. Sketch of the proof; 6.4. Pryce s result on bounded
sequences in Z ; 6.5. Sublinear functionals; 6.6. James1
double limit-theorem; 6.7. The double-limit inequality;
6.9. and 6.10. Sets with interchangeable double-limits in lx;
6.11. Attaining the supremum on a subset.
Exercises: 6.20. Pointwise convergence in C(X), X pseudo-
compact: Simons result.
§ 7 Applications of the sup-theorem 82
7.1. Krein s theorem on the convex hull of compact sets;
7.3. and 7.4. Closed sums of convex sets; 7.5. On the unit
ball of Banach-spaces; 7.6. The convex hull of two convex
sets; 7.7. Separation of convex sets; 7.8. Range of vector-
measures; 7.9. Fixed points; 7.10. Peano s theorem in non-
reflexive Banach-spaces.
Exercises: 7.13. Interchangeable double-limits of the convex
hull; 7.30. Representation of weakly compact operators;
7.31. Uniformly convex spaces.
§8 The topology related to Rainwater s theorem 98
8.1. Rainwater s theorem in Choquet-theory and Tweddle s idea;
8.2. The weak topology coming from extreme points of equi-
continuous sets; 8.3. Compactness results; 8.4. Pointwise
VII
convergence; 8.5. Weak convergence in L ; 8.6. Uniformly
integrable sets; 8.7. Schur s lemma; 8.9. Dunford-Pettis
characterisation of weak compactness in iA; 8.10. - 8.12.
e-tensor products; 8.13. Vector-valued continuous and
differentiable functions.
Exercises: 8.23. Measures with densities; 8.24. Convergence
in measure.
Bibliography 117
References to the sections 120
List of symbols and spaces 121
Index 122
|
| any_adam_object | 1 |
| author | Floret, Klaus |
| author_facet | Floret, Klaus |
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| author_sort | Floret, Klaus |
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| callnumber-raw | QA3 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)6378609 (DE-599)BVBBV002261593 |
| dewey-full | 515.7/3 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515.7/3 510 |
| dewey-search | 515.7/3 510 |
| dewey-sort | 3515.7 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002261593 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:42:58Z |
| institution | BVB |
| isbn | 3540099913 0387099913 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001486258 |
| oclc_num | 6378609 |
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| physical | VII, 123 S. |
| publishDate | 1980 |
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| publishDateSort | 1980 |
| publisher | Springer |
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| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Floret, Klaus Verfasser aut Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 Klaus Floret Berlin [u.a.] Springer 1980 VII, 123 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 801 Espaces compacts Espaces localement convexes Espaces vectoriels topologiques Compact spaces Linear topological spaces Locally convex spaces Schwach kompakte Menge (DE-588)4180289-5 gnd rswk-swf Kompakte Menge (DE-588)4164849-3 gnd rswk-swf Schwach kompakte Menge (DE-588)4180289-5 s DE-604 Kompakte Menge (DE-588)4164849-3 s Lecture notes in mathematics 801 (DE-604)BV000676446 801 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Floret, Klaus Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 Lecture notes in mathematics Espaces compacts Espaces localement convexes Espaces vectoriels topologiques Compact spaces Linear topological spaces Locally convex spaces Schwach kompakte Menge (DE-588)4180289-5 gnd Kompakte Menge (DE-588)4164849-3 gnd |
| subject_GND | (DE-588)4180289-5 (DE-588)4164849-3 |
| title | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 |
| title_auth | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 |
| title_exact_search | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 |
| title_full | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 Klaus Floret |
| title_fullStr | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 Klaus Floret |
| title_full_unstemmed | Weakly compact sets lectures held at S.U.N.Y., Buffalo, in Spring 1978 Klaus Floret |
| title_short | Weakly compact sets |
| title_sort | weakly compact sets lectures held at s u n y buffalo in spring 1978 |
| title_sub | lectures held at S.U.N.Y., Buffalo, in Spring 1978 |
| topic | Espaces compacts Espaces localement convexes Espaces vectoriels topologiques Compact spaces Linear topological spaces Locally convex spaces Schwach kompakte Menge (DE-588)4180289-5 gnd Kompakte Menge (DE-588)4164849-3 gnd |
| topic_facet | Espaces compacts Espaces localement convexes Espaces vectoriels topologiques Compact spaces Linear topological spaces Locally convex spaces Schwach kompakte Menge Kompakte Menge |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001486258&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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