Factorization of linear operators and geometry of Banach spaces: [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984]
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Math. Soc.
1986
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| Series: | Regional conference series in mathematics
60 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 154 S. |
| ISBN: | 0821807102 |
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MARC
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| 245 | 1 | 0 | |a Factorization of linear operators and geometry of Banach spaces |b [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] |c Gilles Pisier |
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Record in the Search Index
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| adam_text | Contents
Introduction vii
Chapter 0. Preliminary Results and Background 1
a. General notation 1
b. An introduction to tensor products. The approximation property.
Nuclear operators 2
c. Local reflexivity 6
Chapter 1. Absolutely Summing Operators and Basic Applications 9
a. Absolutely summing operators 9
b. Applications to Banach spaces 16
c. An introduction to duality theory. Integral operators 18
Notes and references 19
Chapter 2. Factorization through a Hilbert Space 21
a. Operators factoring through a Hilbert space 21
b. A duality theorem 25
Notes and references 30
Chapter 3. Type and Cotype. Kwapieh s Theorem 31
a. Type and cotype. Definitions 31
b. Kwapieh s theorem 32
c. Supplementary results 34
d. Type and cotype and the geometry of Banach spaces 38
Notes and references 40
Chapter 4. The Abstract Version of Grothendieck s Theorem 41
a. The factorization theorem 41
b. An application to harmonic analysis 49
Notes and references 51
v
Vi CONTENTS
Chapter 5. Grothendieck s Theorem 53
a. Preliminaries. Localization techniques. J ^ spaces 53
b. Operators on C( K ) spaces 54
c. Operators on Lx spaces 57
d. Cotype 2 spaces and absolutely summing operators 62
e. Best constants. Krivine s proof 64
f. A proof of G.T. using harmonic analysis 68
Notes and references 69
Chapter 6. Banach Spaces Satisfying Grothendieck s Theorem 71
a. G.T. spaces 71
b. G.T. spaces of cotype 2 73
c. Quotients of L, by a reflexive subspace 78
d. Bourgain s theorem on L1/H1 83
Notes and references 86
Chapter 7. Applications of the Volume Ratio Method 89
Notes and references 95
Chapter 8. Banach Lattices 97
a. The Banach lattice version of G.T. 97
b. Ultraproducts. Factorization through an Lp space 101
c. Local unconditional structure. The Gordon Lewis property 104
d. Examples of Banach spaces without l.u.st. 108
e. Finite dimensional spaces with extreme l.u.st. constants 113
f. G.T. spaces with unconditional basis 114
g. Infinite dimensional Kasin decompositions 114
Notes and references 118
Chapter 9. C * Algebras 119
a. The noncommutative version of G.T. 119
b. Applications 130
Notes and references 132
Chapter 10. Counterexamples to Grothendieck s Conjecture 135
a. Outline of the construction 135
b. Extensions of a Banach space 137
c. The construction 140
d. Particular cases of the conjectures 145
e. Some open problems 146
Notes and references 147
References 149
|
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| author | Pisier, Gilles 1950- |
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| bvnumber | BV000606956 |
| classification_rvk | SI 195 SK 600 SK 620 |
| classification_tum | MAT 462f |
| ctrlnum | (OCoLC)260086880 (DE-599)BVBBV000606956 |
| discipline | Mathematik |
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| id | DE-604.BV000606956 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:16:29Z |
| institution | BVB |
| isbn | 0821807102 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000377581 |
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| physical | X, 154 S. |
| publishDate | 1986 |
| publishDateSearch | 1986 |
| publishDateSort | 1986 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Regional conference series in mathematics |
| series2 | Regional conference series in mathematics |
| spelling | Pisier, Gilles 1950- Verfasser (DE-588)113782268 aut Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] Gilles Pisier Providence, RI American Math. Soc. 1986 X, 154 S. txt rdacontent n rdamedia nc rdacarrier Regional conference series in mathematics 60 Linearer Operator (DE-588)4167721-3 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Faktorisierung (DE-588)4128927-4 gnd rswk-swf Linearer Operator (DE-588)4167721-3 s Faktorisierung (DE-588)4128927-4 s Banach-Raum (DE-588)4004402-6 s DE-604 Regional conference series in mathematics 60 (DE-604)BV000004346 60 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000377581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pisier, Gilles 1950- Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] Regional conference series in mathematics Linearer Operator (DE-588)4167721-3 gnd Banach-Raum (DE-588)4004402-6 gnd Faktorisierung (DE-588)4128927-4 gnd |
| subject_GND | (DE-588)4167721-3 (DE-588)4004402-6 (DE-588)4128927-4 |
| title | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] |
| title_auth | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] |
| title_exact_search | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] |
| title_full | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] Gilles Pisier |
| title_fullStr | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] Gilles Pisier |
| title_full_unstemmed | Factorization of linear operators and geometry of Banach spaces [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] Gilles Pisier |
| title_short | Factorization of linear operators and geometry of Banach spaces |
| title_sort | factorization of linear operators and geometry of banach spaces expository lectures from the cbms regional conference held at the university of missouri columbia june 25 29 1984 |
| title_sub | [expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25 - 29, 1984] |
| topic | Linearer Operator (DE-588)4167721-3 gnd Banach-Raum (DE-588)4004402-6 gnd Faktorisierung (DE-588)4128927-4 gnd |
| topic_facet | Linearer Operator Banach-Raum Faktorisierung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000377581&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004346 |
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