Narrow operators on function spaces and vector lattices:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
de Gruyter
2013
|
| Series: | De Gruyter studies in mathematics
45 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | XIII, 319 S. |
| ISBN: | 3110263033 9783110263039 |
Staff View
MARC
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| 300 | |a XIII, 319 S. | ||
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Record in the Search Index
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IMAGE 1
CONTENTS
PREFACE VII
1 INTRODUCTION AND PRELIMINARIES 1
1.1 BACKGROUND INFORMATION 1
1.2 TERMINOLOGY AND NOTATION 1
1.3 NARROW OPERATORS ON FUNCTION SPACES 2
1.4 HOMOGENEOUS MEASURE SPACES AND MAHARAM'S THEOREM 9
1.5 NECESSARY INFORMATION ON VECTOR LATTICES 12
1.6 KALTON'S AND ROSENTHAL'S REPRESENTATION THEOREMS FOR OPERATORS ON L
\ 21
2 EACH "SMALL" OPERATOR IS NARROW 24
2.1 AM-COMPACT AND DUNFORD-PETTIS OPERATORS ARE NARROW 24
2.2 "LARGE" SUBSPACES ARE EXACTLY STRICTLY RICH 26
2.3 OPERATORS WITH "SMALL" RANGES ARE NARROW 28
2.4 NARROW OPERATORS ARE COMPACT ON A SUITABLE SUBSPACE 32
3 APPLICATIONS TO NONLOCALLY CONVEX SPACES 36
3.1 NONEXISTENCE O F NONZERO NARROW OPERATORS 37
3.2 THE SEPARABLE QUOTIENT SPACE PROBLEM 38
3.3 ISOMORPHIC CLASSIFICATION O F STRONGLY NONCONVEX KOTHE F-SPACES 38
4 NONCOMPACT NARROW OPERATORS 41
4.1 CONDITIONAL EXPECTATION OPERATORS 42
4.2 A NARROW PROJECTION FROM E ONTO A SUBSPACE ISOMETRIC TO 43
4.3 A CHARACTERIZATION O F NARROW CONDITIONAL EXPECTATIONS 51
5 IDEAL PROPERTIES, CONJUGATES, SPECTRUM AND NUMERICAL RADII 57
5.1 IDEAL PROPERTIES OF NARROW OPERATORS AND STABILITY OF RICH SUBSPACES
. . 57
5.2 CONJUGATES OF NARROW OPERATORS NEED NOT BE NARROW 60
5.3 SPECTRUM O F A NARROW OPERATOR 60
5.4 NUMERICAL RADII O F NARROW OPERATORS ON LP(^)-SPACES 62
HTTP://D-NB.INFO/1024907139
IMAGE 2
XII
CONTENTS
6 DAUGAVET-TYPE PROPERTIES O F LEBESGUE AND LORENTZ SPACES 71
6.1 A GENERALIZATION O F THE DP FOR L \ TO "SMALL" INTO ISOMORPHISMS 72
6.2 PSEUDO-DAUGAVET PROPERTY FOR NARROW OPERATORS ON L P , P ^ 2 77
6.3 A PSEUDO-DAUGAVET PROPERTY FOR NARROW PROJECTIONS IN LORENTZ SPACES
89
6.4 NEAR ISOMETRIC CLASSIFICATION OF L^F/IJ-SPACES FOR 1 P OO, P ^ 2
104
7 STRICT SINGULARITY VERSUS NARROWNESS 109
7.1 BOURGAIN-ROSENTHAL'S THEOREM ON L\-STRICTLY SINGULAR OPERATORS I L L
7.2 ROSENTHAL'S CHARACTERIZATION OF NARROW OPERATORS ON L \ 132
7.3 JOHNSON-MAUREY-SCHECHTMAN-TZAFRIRI'S THEOREM 150
7.4 AN APPLICATION TO ALMOST ISOMETRIC COPIES O F L \ 171
7.5 AN APPLICATION TO COMPLEMENTED SUBSPACES O F L P 173
7.6 THE DAUGAVET PROPERTY FOR RICH SUBSPACES O F L I 174
8 WEAK EMBEDDINGS O F L I 179
8.1 DEFINITIONS 179
8.2 EMBEDDABILITY O F L \ 181
8.3 EXAMPLES 184
8.4 G$ -EMBEDDINGS O F L \ ARE NOT NARROW 190
8.5 SIGN-EMBEDDABILITY O F L I DOES NOT IMPLY ISOMORPHIC EMBEDDABILITY
194
9 SPACES X FOR WHICH EVERY OPERATOR T E ( L P , A') IS NARROW 210
9.1 A CHARACTERIZATION USING THE RANGES O F VECTOR MEASURES 210
9.2 EVERY OPERATOR FROM E TO C O ( R ) IS NARROW 214
9.3 AN ANALOG O F THE PITT COMPACTNESS THEOREM FOR L P -SPACES 215
9.4 WHEN IS EVERY OPERATOR FROM L P TO L R NARROW? 216
9.5 ^2-STRICTLY SINGULAR OPERATORS ON L P 225
10 NARROW OPERATORS ON VECTOR LATTICES 229
10.1 TWO DEFINITIONS OF A NARROW OPERATOR ON VECTOR LATTICES 230
10.2 AM-COMPACT ORDER-TO-NORM CONTINUOUS OPERATORS ARE NARROW 234
10.3 T IS NARROW IF AND ONLY IF | T | IS NARROW 238
10.4 THE ENFLO-STARBIRD FUNCTION AND A-NARROW OPERATORS 241
10.5 CLASSICAL THEOREMS 243
10.6 PSEUDONARROW OPERATORS ARE EXACTLY A-NARROW OPERATORS 246
10.7 REGULAR NARROW OPERATORS FORM A BAND IN THE LATTICE OF REGULAR
OPERATORS 250
IMAGE 3
CONTENTS XIII
10.8 NARROW OPERATORS ON LATTICE-NORMED SPACES 252
10.9 ^-STRICTLY SINGULAR REGULAR OPERATORS ARE NARROW 260
11 SOME VARIANTS O F THE NOTION O F NARROW OPERATORS 265
11.1 HEREDITARILY NARROW OPERATORS 266
11.2 GENTLE NARROW OPERATORS ON L P WITH \ P 2 274
11.3 C-NARROW OPERATORS ON C(K)~ SPACES 281
11.4 NARROW OPERATORS ON LOO (/I)-SPACES 289
11.5 NARROW 2-HOMOGENEOUS POLYNOMIALS 301
12 OPEN PROBLEMS 303
BIBLIOGRAPHY 307
INDEX OF NAMES 315
SUBJECT INDEX 317 |
| any_adam_object | 1 |
| author | Popov, Michail B. Randrianantoanina, Beata |
| author_GND | (DE-588)133643972 |
| author_facet | Popov, Michail B. Randrianantoanina, Beata |
| author_role | aut aut |
| author_sort | Popov, Michail B. |
| author_variant | m b p mb mbp b r br |
| building | Verbundindex |
| bvnumber | BV040604348 |
| classification_rvk | SK 620 |
| ctrlnum | (OCoLC)820627210 (DE-599)DNB1024907139 |
| dewey-full | 515.724 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040604348 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-21T00:22:15Z |
| institution | BVB |
| isbn | 3110263033 9783110263039 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025432045 |
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| physical | XIII, 319 S. |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Popov, Michail B. Verfasser aut Narrow operators on function spaces and vector lattices Mikhail Popov ; Beata Randrianantoanina Berlin [u.a.] de Gruyter 2013 XIII, 319 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 45 Vektorverband (DE-588)4187471-7 gnd rswk-swf Operator (DE-588)4130529-2 gnd rswk-swf Funktionenraum (DE-588)4134834-5 gnd rswk-swf Operator (DE-588)4130529-2 s Funktionenraum (DE-588)4134834-5 s Vektorverband (DE-588)4187471-7 s DE-604 Randrianantoanina, Beata Verfasser (DE-588)133643972 aut Erscheint auch als Online-Ausgabe 978-3-11-026334-3 De Gruyter studies in mathematics 45 (DE-604)BV000005407 45 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4097371&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Popov, Michail B. Randrianantoanina, Beata Narrow operators on function spaces and vector lattices De Gruyter studies in mathematics Vektorverband (DE-588)4187471-7 gnd Operator (DE-588)4130529-2 gnd Funktionenraum (DE-588)4134834-5 gnd |
| subject_GND | (DE-588)4187471-7 (DE-588)4130529-2 (DE-588)4134834-5 |
| title | Narrow operators on function spaces and vector lattices |
| title_auth | Narrow operators on function spaces and vector lattices |
| title_exact_search | Narrow operators on function spaces and vector lattices |
| title_full | Narrow operators on function spaces and vector lattices Mikhail Popov ; Beata Randrianantoanina |
| title_fullStr | Narrow operators on function spaces and vector lattices Mikhail Popov ; Beata Randrianantoanina |
| title_full_unstemmed | Narrow operators on function spaces and vector lattices Mikhail Popov ; Beata Randrianantoanina |
| title_short | Narrow operators on function spaces and vector lattices |
| title_sort | narrow operators on function spaces and vector lattices |
| topic | Vektorverband (DE-588)4187471-7 gnd Operator (DE-588)4130529-2 gnd Funktionenraum (DE-588)4134834-5 gnd |
| topic_facet | Vektorverband Operator Funktionenraum |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4097371&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025432045&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT popovmichailb narrowoperatorsonfunctionspacesandvectorlattices AT randrianantoaninabeata narrowoperatorsonfunctionspacesandvectorlattices |