Geometry and probability in Banach spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin, [u.a.]
Springer
1981
|
| Series: | Lecture notes in mathematics
852 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 101 Seiten Illustrationen |
| ISBN: | 354010691X 038710691X |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometry and probability in Banach spaces |c Laurent Schwartz, Notes by Paul R. Chernoff |
| 264 | 1 | |a Berlin, [u.a.] |b Springer |c 1981 | |
| 300 | |a X, 101 Seiten |b Illustrationen | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 852 | |
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| 650 | 4 | |a Opérateurs linéaires | |
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| 650 | 4 | |a Probabilités | |
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| 650 | 4 | |a Probabilities | |
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Record in the Search Index
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| adam_text |
Contents
I. Introduction 1
Lecture 1. Type and cotype for a Banach space 1
p-summing maps 1
Lecture 2. Pietsch factorization theorem 5
Lecture 3. Completely summing maps 9
Hilbert-Schmidt and nuclear maps 9
Lecture 4. p-integral maps 15
II. Cylindrical Probabilities and Radonifying Maps 18
Lecture 5. Completely summing maps: 6 equivalent properties 20
p-Radonifying maps 20
Lecture 6. Radonification Theorem 25
Lecture 7. p-Gauss laws 29
Lecture 8. proof of the Pietsch conjecture 32
Lecture 9. p-Pietsch spaces 38
Application: Brownian motion 38
Lecture 10 More on cylindrical measures and stochastic processes 42
III. Types and Cotypes 46
Lecture 11. Kahane inequality 47
The case of Lp 47
Z-type 47
Lecture 12. Kahane contraction principle 51
p-Gauss type 51
The Gauss type interval is open 51
X
IV. Ultrapowers and Superproperties 56
Lecture 12. Finite representability of F in E 56
Superproperties 57
The "spectrum" of a Banach space 57
Lecture 13. q-factorization, Maurey's theorem 58
Grothendieck factorization theorem 58
Lecture 14. Equivalent properties, summing vs. factorization 61
Lecture 15. Non-existence of (2+e)-Pietsch spaces 67
Ultrapowers 67
Lecture 16. The Pietsch interval 72
The weakest non-trivial superproperty 72
Cotypes, Rademacher vs. Gauss 72
Lecture 17. Gauss-summing maps 78
Grothendieck factorization theorem (a=+°°) 81
TLC and ILL 83
Lecture 18. Super-reflexive spaces 85
Modulus of convexity, q-convexity 85
"Trees" and Kelly-Chatteryji Theorem 85
Enflo Theorem 85
Modulus of smoothness, p-smoothness 85
Properties equivalent to super-reflexivity 85
Lecture 19. Martingale type and cotype 92
Results of Pisier 92
Twelve properties equivalent to super-reflexivity 92
Type for subspaces of Lp (Rosenthal Theorem) 92
A new result of Pisier 98
REFERENCES 99
INDEX 100 |
| any_adam_object | 1 |
| author | Schwartz, Laurent 1915-2002 |
| author_GND | (DE-588)118795694 |
| author_facet | Schwartz, Laurent 1915-2002 |
| author_role | aut |
| author_sort | Schwartz, Laurent 1915-2002 |
| author_variant | l s ls |
| building | Verbundindex |
| bvnumber | BV002266361 |
| callnumber-first | Q - Science |
| callnumber-label | QA3 |
| callnumber-raw | QA3 |
| callnumber-search | QA3 |
| callnumber-sort | QA 13 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 850 |
| ctrlnum | (OCoLC)7462049 (DE-599)BVBBV002266361 |
| dewey-full | 515.7/32 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis 510 - Mathematics |
| dewey-raw | 515.7/32 510 |
| dewey-search | 515.7/32 510 |
| dewey-sort | 3515.7 232 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002266361 |
| illustrated | Illustrated |
| indexdate | 2025-01-27T11:01:01Z |
| institution | BVB |
| isbn | 354010691X 038710691X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001489282 |
| oclc_num | 7462049 |
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| physical | X, 101 Seiten Illustrationen |
| publishDate | 1981 |
| publishDateSearch | 1981 |
| publishDateSort | 1981 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Schwartz, Laurent 1915-2002 (DE-588)118795694 aut Geometry and probability in Banach spaces Laurent Schwartz, Notes by Paul R. Chernoff Berlin, [u.a.] Springer 1981 X, 101 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 852 Banach, Espaces de Banach, espaces de ram Opérateurs linéaires Opérateurs linéaires ram Probabilités Probabilités ram Banach spaces Linear operators Probabilities Banach-Raum (DE-588)4004402-6 gnd rswk-swf Wahrscheinlichkeit (DE-588)4137007-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Geometrie (DE-588)4020236-7 s Wahrscheinlichkeit (DE-588)4137007-7 s Erscheint auch als Online-Ausgabe 978-3-540-10691-3 Lecture notes in mathematics 852 (DE-604)BV000676446 852 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schwartz, Laurent 1915-2002 Geometry and probability in Banach spaces Lecture notes in mathematics Banach, Espaces de Banach, espaces de ram Opérateurs linéaires Opérateurs linéaires ram Probabilités Probabilités ram Banach spaces Linear operators Probabilities Banach-Raum (DE-588)4004402-6 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Geometrie (DE-588)4020236-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4137007-7 (DE-588)4020236-7 (DE-588)4064324-4 |
| title | Geometry and probability in Banach spaces |
| title_auth | Geometry and probability in Banach spaces |
| title_exact_search | Geometry and probability in Banach spaces |
| title_full | Geometry and probability in Banach spaces Laurent Schwartz, Notes by Paul R. Chernoff |
| title_fullStr | Geometry and probability in Banach spaces Laurent Schwartz, Notes by Paul R. Chernoff |
| title_full_unstemmed | Geometry and probability in Banach spaces Laurent Schwartz, Notes by Paul R. Chernoff |
| title_short | Geometry and probability in Banach spaces |
| title_sort | geometry and probability in banach spaces |
| topic | Banach, Espaces de Banach, espaces de ram Opérateurs linéaires Opérateurs linéaires ram Probabilités Probabilités ram Banach spaces Linear operators Probabilities Banach-Raum (DE-588)4004402-6 gnd Wahrscheinlichkeit (DE-588)4137007-7 gnd Geometrie (DE-588)4020236-7 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Banach, Espaces de Banach, espaces de Opérateurs linéaires Probabilités Banach spaces Linear operators Probabilities Banach-Raum Wahrscheinlichkeit Geometrie Wahrscheinlichkeitsrechnung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001489282&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT schwartzlaurent geometryandprobabilityinbanachspaces |