Functional analysis and infinite dimensional geometry:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2001
|
| Schriftenreihe: | CMS books in mathematics
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 431 - 443 |
| Beschreibung: | IX, 451 S. 25 cm |
| ISBN: | 0387952195 |
Internformat
MARC
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| 245 | 1 | 0 | |a Functional analysis and infinite dimensional geometry |c Marián Fabian ... |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2001 | |
| 300 | |a IX, 451 S. |b 25 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a CMS books in mathematics |v 8 | |
| 500 | |a Literaturverz. S. 431 - 443 | ||
| 650 | 4 | |a Analyse fonctionnelle | |
| 650 | 7 | |a Análise funcional |2 larpcal | |
| 650 | 4 | |a Banach, Espaces de | |
| 650 | 7 | |a Espaços de banach |2 larpcal | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Functional analysis | |
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| 689 | 1 | |5 DE-604 | |
| 700 | 1 | |a Fabian, Marián J. |e Sonstige |0 (DE-588)123072093 |4 oth | |
| 830 | 0 | |a CMS books in mathematics |v 8 |w (DE-604)BV013248581 |9 8 | |
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Datensatz im Suchindex
| _version_ | 1804128747329159168 |
|---|---|
| adam_text | Contents
Preface v
1 Basic Concepts in Banach Spaces 1
Holder and Minkowski inequalities, classical spaces C[0,1], £p, cq,
LP[Q,1], 2
Operators, quotient spaces, finite dimensional spaces, Riesz s
lemma, separability 10
Hilbert spaces, orthonormal bases, £2 16
Exercises 21
2 Hahn Banach and Banach Open Mapping Theorems 37
Hahn Banach extension and separation theorems 38
Duals of classical spaces 44
Banach open mapping theorem, closed graph theorem, dual
operators 49
Exercises 52
3 Weak Topologies 63
Weak and weak star topology, Banach Steinhaus uniform
boundedness principle, Alaoglu s and Goldstine s theorem,
reflexivity 64
Extreme points, Krein Milman theorem, James boundary,
Ekeland s variational principle, Bishop Phelps theorem . 76
Exercises 86
viii Contents
4 Locally Convex Spaces 107
Local bases, bounded sets, metrizability and normability,
finite dimensional spaces, distributions 108
Bipolar theorem, Mackey topology 116
Caratheodory and Choquet representation; Banach Dieudonne,
Eberlein Smulian, Kaplansky theorems, and Banach Stone
theorem 121
Exercises 130
5 Structure of Banach Spaces 137
Projections and complementability, Auerbach bases 137
Separable spaces as subspaces of C[0,1] and quotients of £ ,
Sobczyk s theorem, Schur s property of (, 140
Exercises 147
6 Schauder Bases 161
Shrinking and boundedly complete bases, reflexivity, Mazur s
basic sequence theorem, small perturbation lemma . . . 165
Block basis sequences, Pelczynski s decomposition method and
subspaces of £p, Pitt s theorem, Khintchine s inequality and
subspaces of Lp 172
Unconditional bases, James s theorem on containment of l and
Co, James s space J, Bessaga Pekzynski theorem .... 180
Markushevich bases in separable spaces, their extension property,
Johnson s and Plichko s result on £« 188
Exercises 191
7 Compact Operators on Banach Spaces 203
Compact and finite rank operators, Fredholm operators,
Fredholm alternative 203
Eigenvalues, eigenspaces, spectrum, spectral decomposition . . 210
Spectral theory of compact self adjoint and compact normal
operators 216
Banach s contraction principle, nonexpansive mappings, Ryll
Nardzewski theorem, Brouwer s and Schauder s theorems,
invariant subspaces 227
Exercises 231
8 Differentiability of Norms 241
Smulian s dual test, Kadec s Frechet smooth renorming of spaces
with separable dual, Frechet differentiability of convex
functions 243
More on extremal structure, Lindenstrauss s result on strongly
exposed points and norm attaining operators 255
Exercises 263
Contents ix
9 Uniform Convexity 285
Uniform convexity and uniform smoothness, £p spaces 285
Finite representability, local reflexivity, superreflexive spaces and
Enflo s renorming, Kadec s and Gurarii Gurarii James
theorems 291
Exercises 305
10 Smoothness and Structure 313
Smooth and compact variational principles, subdifFerential,
Stegall s variational principle 314
Partitions of unity, smooth approximation 328
Lipschitz homeomorphisms, Aharoni s embeddings into cq,
Heinrich Mankiewicz results on linearization of Lipschitz
maps 331
Homeomorphisms, Mazur s theorem on £p, Kadec s theorem . . 336
Smoothness in £p and Hilbert spaces 340
Countable James boundary and saturation by cq 343
Exercises 346
11 Weakly Compactly Generated Spaces 357
Projectional resolutions, injections into co(F), Eberlein compacts,
embedding into a reflexive space, locally uniformly rotund
and smooth renormings 358
Weakly compact operators, Davis Figiel Johnson Pelczyriski
factorization, absolutely summing operators, Pietsch
factorization, Dunford Pettis property 370
Quasicomplements 377
Exercises 379
12 Topics in Weak Topology 387
Eberlein compacts, metrizable subspaces 388
Uniform Eberlein compacts, scattered compacts 394
Weakly Lindelof spaces, property C 402
Corson compacts, weak pseudocompactness in Banach spaces,
(Bx, w) Polish 409
Exercises 417
References 431
Index 445
|
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| discipline | Mathematik |
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| id | DE-604.BV013902371 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:54:09Z |
| institution | BVB |
| isbn | 0387952195 |
| language | English |
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| physical | IX, 451 S. 25 cm |
| publishDate | 2001 |
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| publisher | Springer |
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| series | CMS books in mathematics |
| series2 | CMS books in mathematics |
| spelling | Functional analysis and infinite dimensional geometry Marián Fabian ... New York [u.a.] Springer 2001 IX, 451 S. 25 cm txt rdacontent n rdamedia nc rdacarrier CMS books in mathematics 8 Literaturverz. S. 431 - 443 Analyse fonctionnelle Análise funcional larpcal Banach, Espaces de Espaços de banach larpcal Banach spaces Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Banach-Raum (DE-588)4004402-6 s Fabian, Marián J. Sonstige (DE-588)123072093 oth CMS books in mathematics 8 (DE-604)BV013248581 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Functional analysis and infinite dimensional geometry CMS books in mathematics Analyse fonctionnelle Análise funcional larpcal Banach, Espaces de Espaços de banach larpcal Banach spaces Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4004402-6 |
| title | Functional analysis and infinite dimensional geometry |
| title_auth | Functional analysis and infinite dimensional geometry |
| title_exact_search | Functional analysis and infinite dimensional geometry |
| title_full | Functional analysis and infinite dimensional geometry Marián Fabian ... |
| title_fullStr | Functional analysis and infinite dimensional geometry Marián Fabian ... |
| title_full_unstemmed | Functional analysis and infinite dimensional geometry Marián Fabian ... |
| title_short | Functional analysis and infinite dimensional geometry |
| title_sort | functional analysis and infinite dimensional geometry |
| topic | Analyse fonctionnelle Análise funcional larpcal Banach, Espaces de Espaços de banach larpcal Banach spaces Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Analyse fonctionnelle Análise funcional Banach, Espaces de Espaços de banach Banach spaces Functional analysis Funktionalanalysis Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009514206&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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