Banach spaces for analysts:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Ausgabe: | 1. paperback ed., transferred to digital print. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 382 S. |
| ISBN: | 9780521566759 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents Preface ix Part I. Introduction LA. LB. Functional analysis Examples of spaces and operators 3 9 Part II. Basic concepts of Banach space theory ILA. ILB. ILC. ILD. ILE. Weak topologies Weak and weak* topologies, Mazur’s, Alaoglu’s and Goldstine’s theorems, reflexive spaces Isomorphisms, bases, projections Banach-Mazur theorem, block-bases and selection of block basic subsequences, examples of bases: Haar, FaberSchauder and trigonometric systems, small perturbations of basic sequences, decomposition method Weak compactness Eberlein-Smulian theorem, weakly compact operators; their factorization and basic properties Convergence of series Definitions and characterizations of unconditionally and weakly unconditionally convergent series, Orlicz theorem and Orlicz property, unconditional bases, spaces without unconditional basis, the Haar system is an unconditional basis in Lp for 1 p oo Local properties Bounded approximation property and тгд-ѕрасеѕ, BanachMazur distance and distances between -spaces and spaces of trigonometric polynomials, good ε-nets in Βχ, Auerbach lemma, principle of local reflexivity 27 35 49 57 69 Part III. Selected topics ULA. Ар-spaces; type and cotype Sobolev spaces (1 p oo) and Bergman spaces (1 p oo) are isomorphic to Lp-spaces, complemented subspaces of £p, stable laws and embeddings of £p into 83
vi III.B III.C. III.D. IILE. ULF. Contents Lq, О q p 2, type and cotype, Kahane’s inequality, types and cotypes of Lp-spaces, Carleman theorem, Banach-Saks theorem. Projection constants Loo is injective, extension and projection constants, Lewis’s theorem on projections in Lp, Kadec-Snobar theorem, projection constants of various spaces of polynomials, existence of an inner function on the ball in (Cd, polynomial bases in C(T), projective tensor products and dual treatment of extensions of operators Li ^)-spaces Semi-embeddings and the non-existence of semi embeddings of Li [0,1] into co, Menchoff theorem, Lyons theorem characterizing zero sets for measures with Fourier transforms tending to zero, Schur theorem that weakly compact sets in ¿i axe compact, uniform integrability and characterization of weakly compact sets in Li(p), weak sequential completeness of Li {μ), finite representability of ¿i in a Banach space; connections with type, reflexive subspaces of Li (μ), Nevanlinna theorem on unimodular functions in cosets of Loo/Hoo C(K)-spaces M-ideals and best approximation, Hoo + C is a closed algebra, (Hoo + C)/Hoo is an M-ideal in Loo/Hoo, Michael-Pelczyński linear extension theorem, Milutin theorem, Franklin system - construction and basic properties, LipafTT) is isomorphic to too, Dunford-Pettis property for rich subspaces of C(K), in particular for ball algebras and Sobolev spaces The disc algebra Rudin-Carleson theorem, interpolating sequences, interpolation of continuous functions by functions with finite Dirichlet integral, lacunary Fourier coefficients of
functions in the disc algebra, projections in A and infinite divisibility of A, existence of basis Absolutely summing and related operators Absolutely summing operators, Grothendieck’s and Pietsch’s theorems, unconditional bases in Li-spaces, local units in Li(G), Grothendieck’s inequality, polynomially bounded but not power-bounded operators, p-nuclear and p-integral operators, trace duality, characterization 111 131 151 181 199
Contents vii of Sidon sets, extrapolation inequalities for spaces of all p-absolutely summing operators, Grothendieck-Maurey theorem, p-absolutely summing operators and cotype 2 237 IILG. Schatten-von Neumann classes Approximation numbers of operators between Banach spaces, Weyl’s inequality, Schatten-von Neumann classes and eigenvalues, Hilbert-Schmidt operators, Fourier coefficients of Hôlder functions, summability of eigenvalues of p-absolutely summing operators between Banach spaces with applications 257 III.H. Factorization theorems Nikishin’s theorem and some applications, Maurey’s factorization of operators into Lp, reflexive subspaces of ¿i, connections between factorization and p-absolutely summing operators, structure of series unconditionally convergent in measure, dilation theorem and connections with orthogonal series, Menchoff-Rademacher theorem on almost everywhere convergence, more about Fourier coefficients of Hôlder functions, some multipliers into Bergman spaces 291 HI.I. Absolutely summing operators on the disc algebra Proper uniform algebras are uncomplemented, Bourgain’s analytic projections onto Hp(AdX), extrapolation inequalities between p-absolutely summing and q֊ integral norms for operators on A, A* has cotype 2 and the Grothendieck theorem holds for A*, extensions of finite rank operators on A, A®A is closed in C(T)®C(T), reflexive subspaces of extrapolation inequalities for the Riesz projection, extension of operators from reflexive subspaces of L-JH into Яоо interpolation for certain bi-analytic functions Hints for the exercises 323 List of
symbols 341 References 345 Index 377
|
| any_adam_object | 1 |
| author | Wojtaszczyk, Przemysław 1940- |
| author_GND | (DE-588)143778927 |
| author_facet | Wojtaszczyk, Przemysław 1940- |
| author_role | aut |
| author_sort | Wojtaszczyk, Przemysław 1940- |
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| building | Verbundindex |
| bvnumber | BV036628135 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)917682010 (DE-599)BVBBV036628135 |
| discipline | Mathematik |
| edition | 1. paperback ed., transferred to digital print. |
| format | Book |
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| id | DE-604.BV036628135 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:44:31Z |
| institution | BVB |
| isbn | 9780521566759 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020548016 |
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| physical | XIII, 382 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Wojtaszczyk, Przemysław 1940- Verfasser (DE-588)143778927 aut Banach spaces for analysts P. Wojtaszczyk 1. paperback ed., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2009 XIII, 382 S. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 25 Banach-Raum (DE-588)4004402-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s DE-604 Cambridge studies in advanced mathematics 25 (DE-604)BV000003678 25 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020548016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wojtaszczyk, Przemysław 1940- Banach spaces for analysts Cambridge studies in advanced mathematics Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4004402-6 |
| title | Banach spaces for analysts |
| title_auth | Banach spaces for analysts |
| title_exact_search | Banach spaces for analysts |
| title_full | Banach spaces for analysts P. Wojtaszczyk |
| title_fullStr | Banach spaces for analysts P. Wojtaszczyk |
| title_full_unstemmed | Banach spaces for analysts P. Wojtaszczyk |
| title_short | Banach spaces for analysts |
| title_sort | banach spaces for analysts |
| topic | Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020548016&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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