Banach spaces for analysts:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
1996
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge studies in advanced mathematics
25 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 382 S. graph. Darst. |
| ISBN: | 0521356180 0521566754 |
Staff View
MARC
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| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 1996 | |
| 300 | |a XIII, 382 S. |b graph. Darst. | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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Record in the Search Index
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| adam_text | Contents
Preface ix
Part I. Introduction
LA. Functional analysis 3
I.B. Examples of spaces and operators 9
Part II. Basic concepts of Banach space theory
II.A. Weak topologies 27
Weak and weak* topologies, Mazur s, Alaoglu s and
Goldstine s theorems, reflexive spaces
II.B. Isomorphisms, bases, projections 35
Banach Mazur theorem, block bases and selection of
block basic subsequences, examples of bases: Haar, Faber
Schauder and trigonometric systems, small perturbations
of basic sequences, decomposition method
II.C. Weak compactness 49
Eberlein Smulian theorem, weakly compact operators;
their factorization and basic properties
II.D. Convergence of series 57
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
II.E. Local properties 69
Bounded approximation property and Tr^ spaces, Banach
Mazur distance and distances between £™ spaces and
spaces of trigonometric polynomials, good e nets in Bx,
Auerbach lemma, principle of local reflexivity
Part III. Selected topics
III.A. Lp spaces; type and cotype 83
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
vi Contents
Lq, 0 q p 2, type and cotype, Kahane s inequality,
types and cotypes of Lp spaces, Carleman theorem,
Banach Saks theorem.
III.B Projection constants 111
Lqo 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
III.C. I,i(/x) spaces 131
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 are compact, uniform
integrability and characterization of weakly compact sets
in Li(fi), weak sequential completeness of Li(fi), finite
representability of t in a Banach space; connections
with type, reflexive subspaces of Li(/x), Nevanlinna
theorem on unimodular functions in cosets of L^/H^
III.D. C(*:) spaces 151
M ideals and best approximation, H^ + C is a closed
algebra, (ifoo + C)/i?oo is an M ideal in L^/H^,
Michael Peiczyriski linear extension theorem, Milutin
theorem, Franklin system construction and basic
properties, Lipa(W) is isomorphic to £ *,, Dunford Pettis
property for rich subspaces of C(K), in particular for
ball algebras and Sobolev spaces
III.E. The disc algebra 181
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
III.F. Absolutely summing and related operators 199
Absolutely summing operators, Grothendieck s and
Pietsch s theorems, unconditional bases in Li spaces, local
units in L (G), Grothendieck s inequality, polynomially
bounded but not power bounded operators, p nuclear
and ^ integral operators, trace duality, characterization
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
III.G. Schatten von Neumann classes 237
Approximation numbers of operators between Banach
spaces, Weyl s inequality, Schatten von Neumann
classes and eigenvalues, Hilbert Schmidt operators,
Fourier coefficients of Holder functions, summability of
eigenvalues of p absolutely summing operators between
Banach spaces with applications
III.H. Factorization theorems 257
Nikishin s theorem and some applications, Maurey s
factorization of operators into Lp, reflexive subspaces of
L , 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 Holder functions, some multipliers into
Bergman spaces
III.I. Absolutely summing operators on the disc algebra 291
Proper uniform algebras are uncomplemented, Bourgain s
analytic projections onto Hp(Ad ), 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) 8)C(T),
reflexive subspaces of L /Hx, extrapolation inequalities
for the Riesz projection, extension of operators from
reflexive subspaces of L /H into /foe, 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- |
| author_variant | p w pw |
| building | Verbundindex |
| bvnumber | BV011111897 |
| callnumber-first | Q - Science |
| callnumber-label | QA322 |
| callnumber-raw | QA322.2 |
| callnumber-search | QA322.2 |
| callnumber-sort | QA 3322.2 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)36963242 (DE-599)BVBBV011111897 |
| 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 3732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 1. paperback ed. |
| format | Book |
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| id | DE-604.BV011111897 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:04:11Z |
| institution | BVB |
| isbn | 0521356180 0521566754 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007445183 |
| oclc_num | 36963242 |
| open_access_boolean | |
| owner | DE-703 DE-11 |
| owner_facet | DE-703 DE-11 |
| physical | XIII, 382 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| 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. Cambridge [u.a.] Cambridge Univ. Press 1996 XIII, 382 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 25 Banach, Espaces de Banach, espaces de ram Espaces vectoriels ram espace Banach inriac Banach spaces 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 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007445183&sequence=000002&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, Espaces de Banach, espaces de ram Espaces vectoriels ram espace Banach inriac Banach spaces 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, Espaces de Banach, espaces de ram Espaces vectoriels ram espace Banach inriac Banach spaces Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Banach, Espaces de Banach, espaces de Espaces vectoriels espace Banach Banach spaces Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007445183&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT wojtaszczykprzemysław banachspacesforanalysts |