Orthonormal systems and Banach space geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1998
|
| Edition: | 1. publ. |
| Series: | Encyclopedia of mathematics and its applications
70 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 553 S. |
| ISBN: | 0521624622 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS OVTHONORMAL SYSTEMS AND
BANACH SPACE GEOMETRY ALBRECHT PIETSCH & JORG WENZEL UNIVERSITY OF JENA
CAMBRIDGE UNIVERSITY PRESS CONTENTS PREFACE PAGE IX INTRODUCTION 1 0
PRELIMINARIES 4 0.1 BANACH SPACES AND OPERATORS 4 0.2 FINITE DIMENSIONAL
SPACES AND OPERATORS 7 0.3 CLASSICAL SEQUENCE SPACES 8 0.4 CLASSICAL
FUNCTION SPACES 9 0.5 LORENTZ SPACES 13 0.6 INTERPOLATION METHODS 18 0.7
SUMMATION OPERATORS 19 0.8 FINITE REPRESENTABILITY AND ULTRAPOWERS 20
0.9 EXTREME POINTS 21 0.10 VARIOUS TOOLS '" 23 1 IDEAL NORMS AND
OPERATOR IDEALS 25 1.1 IDEAL NORMS , 25 1.2 OPERATOR IDEALS ' 2 8 1.3
CLASSES OF BANACH SPACES 32 2 IDEAL NORMS ASSOCIATED WITH MATRICES 35
2.1 MATRICES 35 2.2 PARSEVAL IDEAL NORMS AND 2-SUMMING OPERATORS 38 2.3
KWAPIEN IDEAL NORMS AND HILBERTIAN OPERATORS ' 47 2.4 IDEAL NORMS
ASSOCIATED WITH HILBERT MATRICES *- 58 3 IDEAL NORMS ASSOCIATED WITH
ORTHONORMAL SYSTEMS 65 3.1 ORTHONORMAL SYSTEMS 66 3.2 KHINTCHINE
CONSTANTS 70 3.3 RIEMANN IDEAL NORMS 72 VI CONTENTS 3.4 DIRICHLET IDEAL
NORMS 76 3.5 ORTHONORMAL SYSTEMS WITH SPECIAL PROPERTIES 85 3.6 TENSOR
PRODUCTS OF ORTHONORMAL SYSTEMS 86 3.7 TYPE AND COTYPE IDEAL NORMS 89
3.8 CHARACTERS ON COMPACT ABELIAN GROUPS - 98 3.9 DISCRETE ORTHONORMAL
SYSTEMS 111 3.10 SOME UNIVERSAL IDEAL NORMS 115 3.11 PARSEVAL IDEAL
NORMS 123 4 RADEMACHER AND GAUSS IDEAL NORMS 126 4.1 RADEMACHER
FUNCTIONS 127 4.2 RADEMACHER TYPE AND COTYPE IDEAL NORMS 131 4.3
OPERATORS OF RADEMACHER TYPE 136 4.4 B-CONVEXITY 143 4.5 OPERATORS OF
RADEMACHER COTYPE 152 . 4.6 MP-CONVEXITY 159 4.7 GAUSSIAN RANDOM
VARIABLES 164 4.8 GAUSS VERSUS RADEMACHER 172 4.9 GAUSS TYPE AND COTYPE
IDEAL NORMS 185 4.10 OPERATORS OF GAUSS TYPE AND COTYPE 190 4.11 SIDON
CONSTANTS 196 4.12 THE DIRICHLET IDEAL NORMS 6(JI N ,R N ) AND 6(S N , S
N ) 207 4.13 INEQUALITIES BETWEEN (# N ,:R N ) AND E(3JN,3 N ) 212 4.14
THE VECTOR-VALUED RADEMACHER PROJECTION 222 4.15 PARSEVAL IDEAL NORMS
AND 7-SUMMING OPERATORS 226 4.16 THE MAUREY-PISIER THEOREM . 233 5 ' -
_ TRIGONOMETRIC IDEAL NORMS 235 5.1 TRIGONOMETRIC FUNCTIONS 236 5.2 THE
DIRICHLET IDEAL NORMS (*,*) \ 241 5.3 HILBERT MATRICES AND
TRIGONOMETRIC SYSTEMS 264 5.4 THE VECTOR-VALUED HILBERT TRANSFORM 269
5.5 FOURIER TYPE AND COTYPE IDEAL NORMS 281 5.6 OPERATORS OF FOURIER
TYPE 288 5.7 OPERATORS OF FOURIER COTYPE 304 5.8 THE VECTOR-VALUED
FOURIER TRANSFORM 305 5.9 FOURIER VERSUS GAUSS AND RADEMACHER 313 6
WALSH IDEAL NORMS 321 6.1 WALSH FUNCTIONS 322 6.2 WALSH TYPE AND COTYPE
IDEAL NORMS 323 6.3 OPERATORS OF WALSH TYPE 325 CONTENTS VII 6.4 WALSH
VERSUS RADEMACHER 331 6.5 WALSH VERSUS FOURIER 341 7 HAAR IDEAL NORMS
344 7.1 MARTINGALES 345 7.2 DYADIC MARTINGALES 347 - 7.3 HAAR FUNCTIONS
353 7.4 HAAR TYPE AND COTYPE IDEAL NORMS 355 7.5 OPERATORS OF HAAR TYPE
364 7.6 SUPER WEAKLY COMPACT OPERATORS 373 7.7 MARTINGALE TYPE IDEAL
NORMS 380 7.8 J-CONVEXITY 390 7.9 UNIFORM Q-CONVEXITY AND UNIFORM
P-SMOOTHNESS 399 7.10 UNIFORM CONVEXITY AND UNIFORM SMOOTHNESS 412 8
UNCONDITIONALITY 429 8.1 UNCONDITIONAL RIEMANN IDEAL NORMS 429 8.2
UNCONDITIONAL DIRICHLET IDEAL NORMS 430 8.3 RANDOM UNCONDITIONALITY 431
8.4 FOURIER UNCONDITIONALITY 432 8.5 HAAR UNCONDITIONALITY/UMD 436 8.6
RANDOM HAAR UNCONDITIONALITY 443 8.7 THE DIRICHLET IDEAL NORMS 6(W N ,YJ
N ) 456 8.8 THE BURKHOLDER-BOURGAIN THEOREM 459 9 MISCELLANEOUS 461 9.1
INTERPOLATION 461 9.2 SCHATTEN-VON NEUMANN SPACES - . 469 9.3 IDEAL
NORMS OF FINITE RANK OPERATORS 475 9.4 ORTHOGONAL POLYNOMIALS 480 9.5
HISTORY . 489 9.6 EPILOGUE '* 502 SUMMARIES 509 LIST OF SYMBOLS 514
BIBLIOGRAPHY 523 INDEX 546 |
| any_adam_object | 1 |
| author | Pietsch, Albrecht 1934-2024 Wenzel, Jörg |
| author_GND | (DE-588)104515996 |
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| building | Verbundindex |
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| dewey-full | 515.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.732 |
| dewey-search | 515.732 |
| dewey-sort | 3515.732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV012284683 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T08:26:48Z |
| institution | BVB |
| isbn | 0521624622 |
| language | English |
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| physical | IX, 553 S. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Pietsch, Albrecht 1934-2024 Verfasser (DE-588)104515996 aut Orthonormal systems and Banach space geometry Albrecht Pietsch & Jörg Wenzel 1. publ. Cambridge [u.a.] Cambridge Univ. Press 1998 IX, 553 S. txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 70 Banach-Raum - Geometrie - Orthonormalsystem Banach-Raum (DE-588)4004402-6 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Geometrie (DE-588)4020236-7 s DE-604 Wenzel, Jörg Verfasser aut Encyclopedia of mathematics and its applications 70 (DE-604)BV000903719 70 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008328460&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pietsch, Albrecht 1934-2024 Wenzel, Jörg Orthonormal systems and Banach space geometry Encyclopedia of mathematics and its applications Banach-Raum - Geometrie - Orthonormalsystem Banach-Raum (DE-588)4004402-6 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4020236-7 |
| title | Orthonormal systems and Banach space geometry |
| title_auth | Orthonormal systems and Banach space geometry |
| title_exact_search | Orthonormal systems and Banach space geometry |
| title_full | Orthonormal systems and Banach space geometry Albrecht Pietsch & Jörg Wenzel |
| title_fullStr | Orthonormal systems and Banach space geometry Albrecht Pietsch & Jörg Wenzel |
| title_full_unstemmed | Orthonormal systems and Banach space geometry Albrecht Pietsch & Jörg Wenzel |
| title_short | Orthonormal systems and Banach space geometry |
| title_sort | orthonormal systems and banach space geometry |
| topic | Banach-Raum - Geometrie - Orthonormalsystem Banach-Raum (DE-588)4004402-6 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Banach-Raum - Geometrie - Orthonormalsystem Banach-Raum Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008328460&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT pietschalbrecht orthonormalsystemsandbanachspacegeometry AT wenzeljorg orthonormalsystemsandbanachspacegeometry |