A course in functional analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Ausgabe: | 2. ed., corr. 4. printing |
| Schriftenreihe: | Graduate texts in mathematics
96 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 399 S. graph. Darst. |
| ISBN: | 3540972455 9780387972459 |
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| 100 | 1 | |a Conway, John B. |d 1939- |e Verfasser |0 (DE-588)110699882 |4 aut | |
| 245 | 1 | 0 | |a A course in functional analysis |c John B. Conway. [Ed. board: S. Axler ...] |
| 250 | |a 2. ed., corr. 4. printing | ||
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
| 300 | |a XVI, 399 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Graduate texts in mathematics |v 96 | |
| 650 | 4 | |a Functional analysis | |
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Datensatz im Suchindex
| _version_ | 1805067849466642432 |
|---|---|
| adam_text |
CONTENTS
PREFACE
VII
PREFACE
TO
THE
SECOND
EDITION
XI
CHAPTER
I
HILBERT
SPACES
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
1
§2.
ORTHOGONALITY
7
§3.
THE
RIESZ
REPRESENTATION
THEOREM
11
§4.
ORTHONORMAL
SETS
OF
VECTORS
AND
BASES
14
§5.
ISOMORPHIC
HILBERT
SPACES
AND
THE
FOURIER
TRANSFORM
FOR
THE
CIRCLE
19
§6.
THE
DIRECT
SUM
OF
HILBERT
SPACES
23
CHAPTER
II
OPERATORS
ON
HILBERT
SPACE
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
26
§2.
THE
ADJOINT
OF
AN
OPERATOR
31
§3.
PROJECTIONS
AND
IDEMPOTENTS;
INVARIANT
AND
REDUCING
SUBSPACES
36
§4.
COMPACT
OPERATORS
41
§5.*
THE
DIAGONALIZATION
OF
COMPACT
SELF-ADJOINT
OPERATORS
46
§6.*
AN
APPLICATION:
STURM-LIOUVILLE
SYSTEMS
49
§7.*
THE
SPECTRAL
THEOREM
AND
FUNCTIONAL
CALCULUS
FOR
COMPACT
NORMAL
OPERATORS
54
§8.*
UNITARY
EQUIVALENCE
FOR
COMPACT
NORMAL
OPERATORS
60
CHAPTER
III
BANACH
SPACES
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
63
§2.
LINEAR
OPERATORS
ON
NORMED
SPACES
67
XIV
CONTENTS
§3.
FINITE
DIMENSIONAL
NORMED
SPACES
69
§4.
QUOTIENTS
AND
PRODUCTS
OF
NORMED
SPACES
70
§5.
LINEAR
FUNCTIONALS
73
§6.
THE
HAHN-BANACH
THEOREM
77
§7.*
AN
APPLICATION:
BANACH
LIMITS
82
§8.*
AN
APPLICATION:
RUNGE
'
S
THEOREM
83
§9.*
AN
APPLICATION:
ORDERED
VECTOR
SPACES
86
§10.
THE
DUAL
OF
A
QUOTIENT
SPACE
AND
A
SUBSPACE
88
§11.
REFLEXIVE
SPACES
89
§12.
THE
OPEN
MAPPING
AND
CLOSED
GRAPH
THEOREMS
90
§13.
COMPLEMENTED
SUBSPACES
OF
A
BANACH
SPACE
93
§14.
THE
PRINCIPLE
OF
UNIFORM
BOUNDEDNESS
95
CHAPTER
IV
LOCALLY
CONVEX
SPACES
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
99
§2.
METRIZABLE
AND
NORMABLE
LOCALLY
CONVEX
SPACES
105
§3.
SOME
GEOMETRIC
CONSEQUENCES
OF
THE
HAHN-BANACH
THEOREM
108
§4.*
SOME
EXAMPLES
OF
THE
DUAL
SPACE
OF
A
LOCALLY
CONVEX
SPACE
114
§5.*
INDUCTIVE
LIMITS
AND
THE
SPACE
OF
DISTRIBUTIONS
116
CHAPTER
V
WEAK
TOPOLOGIES
§1.
DUALITY
124
§2.
THE
DUAL
OF
A
SUBSPACE
AND
A
QUOTIENT
SPACE
128
§3.
ALAOGLU
'
S
THEOREM
130
§4.
REFLEXIVITY
REVISITED
131
§5.
SEPARABILITY
AND
METRIZABILITY
134
§6.*
AN
APPLICATION:
THE
STONE-CECH
COMPACTIFICATION
137
§7.
THE
KREIN-MILMAN
THEOREM
141
§8.
AN
APPLICATION:
THE
STONE-WEIERSTRASS
THEOREM
145
§9.*
THE
SCHAUDER
FIXED
POINT
THEOREM
149
§10.*
THE
RYLL-NARDZEWSKI
FIXED
POINT
THEOREM
151
§11.*
AN
APPLICATION:
HAAR
MEASURE
ON
A
COMPACT
GROUP
154
§12.*
THE
KREIN-SMULIAN
THEOREM
159
§13.*
WEAK
COMPACTNESS
163
CHAPTER
VI
LINEAR
OPERATORS
ON
A
BANACH
SPACE
§1.
THE
ADJOINT
OF
A
LINEAR
OPERATOR
166
§2.*
THE
BANACH-STONE
THEOREM
171
§3.
COMPACT
OPERATORS
173
§4.
INVARIANT
SUBSPACES
178
§5.
WEAKLY
COMPACT
OPERATORS
183
CONTENTS
XV
CHAPTER
VII
BANACH
ALGEBRAS
AND
SPECTRAL
THEORY
FOR
OPERATORS
ON
A
BANACH
SPACE
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
187
§2.
IDEALS
AND
QUOTIENTS
191
§3.
THE
SPECTRUM
195
§4.
THE
RIESZ
FUNCTIONAL
CALCULUS
199
§5.
DEPENDENCE
OF
THE
SPECTRUM
ON
THE
ALGEBRA
205
§6.
THE
SPECTRUM
OF
A
LINEAR
OPERATOR
208
§7.
THE
SPECTRAL
THEORY
OF
A
COMPACT
OPERATOR
214
§8.
ABELIAN
BANACH
ALGEBRAS
218
§9.*
THE
GROUP
ALGEBRA
OF
A
LOCALLY
COMPACT
ABELIAN
GROUP
223
CHAPTER
VIII
C*-ALGEBRAS
§1.
ELEMENTARY
PROPERTIES
AND
EXAMPLES
232
§2.
ABELIAN
C*-ALGEBRAS
AND
THE
FUNCTIONAL
CALCULUS
IN
C*-ALGEBRAS
236
§3.
THE
POSITIVE
ELEMENTS
IN
A
C*-ALGEBRA
240
§4.*
IDEALS
AND
QUOTIENTS
OF
C
'
-ALGEBRAS
245
§5.*
REPRESENTATIONS
OF
C*-ALGEBRAS
AND
THE
GELFAND-NAIMARK-SEGAL
CONSTRUCTION
248
CHAPTER
IX
NORMAL
OPERATORS
ON
HILBERT
SPACE
§1.
SPECTRAL
MEASURES
AND
REPRESENTATIONS
OF
ABELIAN
C*-ALGEBRAS
255
§2.
THE
SPECTRAL
THEOREM
262
§3.
STAR-CYCLIC
NORMAL
OPERATORS
268
§4.
SOME
APPLICATIONS
OF
THE
SPECTRAL
THEOREM
271
§5.
TOPOLOGIES
ON
274
§6.
COMMUTING
OPERATORS
276
§7.
ABELIAN
VON
NEUMANN
ALGEBRAS
281
§8.
THE
FUNCTIONAL
CALCULUS
FOR
NORMAL
OPERATORS:
THE
CONCLUSION
OF
THE
SAGA
285
§9.
INVARIANT
SUBSPACES
FOR
NORMAL
OPERATORS
290
§10.
MULTIPLICITY
THEORY
FOR
NORMAL
OPERATORS:
A
COMPLETE
SET
OF
UNITARY
INVARIANTS
293
CHAPTER
X
UNBOUNDED
OPERATORS
§1.
BASIC
PROPERTIES
AND
EXAMPLES
303
§2.
SYMMETRIC
AND
SELF-ADJOINT
OPERATORS
308
§3.
THE
CAYLEY
TRANSFORM
316
§4.
UNBOUNDED
NORMAL
OPERATORS
AND
THE
SPECTRAL
THEOREM
319
§5.
STONE
'
S
THEOREM
327
§6.
THE
FOURIER
TRANSFORM
AND
DIFFERENTIATION
334
§7.
MOMENTS
343
XVI
CONTENTS
CHAPTER
XI
FREDHOLM
THEORY
§1.
THE
SPECTRUM
REVISITED
347
§2.
FREDHOLM
OPERATORS
349
§3.
THE
FREDHOLM
INDEX
352
§4.
THE
ESSENTIAL
SPECTRUM
358
§5.
THE
COMPONENTS
OF
S
'
S'
362
§6.
A
FINER
ANALYSIS
OF
THE
SPECTRUM
363
APPENDIX
A
PRELIMINARIES
§1.
LINEAR
ALGEBRA
369
§2.
TOPOLOGY
371
APENDIX
B
THE
DUAL
OF
L
P
(/I)
375
APPENDIX
C
THE
DUAL
OF
C
0
(X)
378
BIBLIOGRAPHY
384
LIST
OF
SYMBOLS
391
INDEX
395 |
| any_adam_object | 1 |
| author | Conway, John B. 1939- |
| author_GND | (DE-588)110699882 |
| author_facet | Conway, John B. 1939- |
| author_role | aut |
| author_sort | Conway, John B. 1939- |
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| callnumber-subject | QA - Mathematics |
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| classification_tum | MAT 460f |
| ctrlnum | (OCoLC)36557108 (DE-599)BVBBV011426667 |
| dewey-full | 515/.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.7 |
| dewey-search | 515/.7 |
| dewey-sort | 3515 17 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. ed., corr. 4. printing |
| format | Book |
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| id | DE-604.BV011426667 |
| illustrated | Illustrated |
| indexdate | 2024-07-20T03:40:45Z |
| institution | BVB |
| isbn | 3540972455 9780387972459 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007683455 |
| oclc_num | 36557108 |
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| owner_facet | DE-384 DE-91 DE-BY-TUM DE-29T DE-91G DE-BY-TUM DE-634 DE-11 DE-83 |
| physical | XVI, 399 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut A course in functional analysis John B. Conway. [Ed. board: S. Axler ...] 2. ed., corr. 4. printing New York [u.a.] Springer 1997 XVI, 399 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 96 Functional analysis Banach-Raum (DE-588)4004402-6 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Hilbert-Raum (DE-588)4159850-7 s 1\p DE-604 Banach-Raum (DE-588)4004402-6 s 2\p DE-604 Graduate texts in mathematics 96 (DE-604)BV000000067 96 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007683455&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Conway, John B. 1939- A course in functional analysis Graduate texts in mathematics Functional analysis Banach-Raum (DE-588)4004402-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4159850-7 (DE-588)4018916-8 |
| title | A course in functional analysis |
| title_auth | A course in functional analysis |
| title_exact_search | A course in functional analysis |
| title_full | A course in functional analysis John B. Conway. [Ed. board: S. Axler ...] |
| title_fullStr | A course in functional analysis John B. Conway. [Ed. board: S. Axler ...] |
| title_full_unstemmed | A course in functional analysis John B. Conway. [Ed. board: S. Axler ...] |
| title_short | A course in functional analysis |
| title_sort | a course in functional analysis |
| topic | Functional analysis Banach-Raum (DE-588)4004402-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Banach-Raum Hilbert-Raum Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007683455&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT conwayjohnb acourseinfunctionalanalysis |