An introduction to functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1992
|
| Series: | Pure and applied mathematics
157 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 600 S. |
| ISBN: | 0824786432 |
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MARC
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Record in the Search Index
| _version_ | 1804118920188133376 |
|---|---|
| adam_text | Contents
Preface v
I. Topological Vector Spaces (TVS) 1
1. Definition and Basic Properties 3
2. Quasi normed and Normed Linear Spaces (NLS) 13
3. Metrizable TVS 31
4. Bounded Sets in a TVS 37
5. Linear Operators and Linear Functionals 43
6. Quotient Spaces 59
7. Finite Dimensional TVS 65
II. The Three Basic Principles 71
8. The Hahn Banach Theorem 73
8.1 Applications of the Hahn Banach Theorem in NLS 77
8.2 Banach Limits 86
8.3 The Moment Problem 89
9. The Uniform Boundedness Principle (UBP) 91
9.1 Bilinear Maps 105
9.2 The Nikodym Boundedness Theorem 112
9.3 Fourier Series 119
9.4 Vector Valued Analytic Functions 123
9.5 Summability 125
10. The Open Mapping and Closed Graph Theorems 137
10.1 Schauder Basis 146
ix
x Contents
HI. Locally Convex TVS (LCS) 155
11. Convex Sets 157
12. Separation of Convex Sets 165
13. Locally Convex TVS 169
13.1 Nonliability 182
13.2 Krein Milman Theorem 184
14. Duality and Weak Topologies 189
15. The Bipolar and Banach Alaoglu Theorems 199
16. Duality in NLS 209
17. Polar Topologies 231
18. The Mackey Arens Theorem 237
19. The Strong Topology and the Bidual 243
20. Quasi barrelled Spaces and the Topology /3*(E, E ) 251
20.1 Perfect Sequence Spaces 256
21. Bornological Spaces 261
22. Inductive Limits 267
IV. Linear Operators 277
23. Topologies on Spaces of Linear Operators 279
23.1 The Krein Smulian Theorem 290
24. Barrelled Spaces 295
25. The UBP and Equicontinuity 305
26. The Transpose of a Linear Operator 309
26.1 Banach s Closed Range Theorems 325
26.2 The Closed Graph and Open Mapping Theorems for
LCS 330
26.3 Vector Integration 334
26.4 The Space of Schwartz Distributions 347
26.5 The Lax Milgram Theorem 366
26.6 Distributions with Compact Support 371
26.7 A Classical Theorem of Borel 379
27. Projections 381
28. Compact Operators 387
28.1 Continuity Properties of Compact Operators 397
28.2 Fredholm Alternative 401
28.3 Factoring Compact Operators 405
28.4 Projecting the Bounded Operators onto the Compact
Operators 416
29. Weakly Compact Operators 423
30. Absolutely Summing Operators 431
30.1 The Dvoretsky Rogers Theorem 440
V. Spectral Theory 441
31. The Spectrum of an Operator 443
32. Subdivisions of the Spectrum and Examples 451
33. The Spectrum of a Compact Operator 457
33.1 Invariant Subspaces and Lomonosov s Theorem 461
34. Adjoints in Hilbert space 465
Contents xi
35. Symmetric, Hermitian and Normal Operators 469
36. The Spectral Theorem for Compact Symmetric Operators 485
36.1 Hilbert Schmidt Operators 494
37. Symmetric Operators with Compact Resolvent 501
38. Orthogonal Projections and the Spectral Theorem for
Compact Symmetric Operators 509
39. Sesquilinear Functionals 515
40. The Gelfand Map for Hermitian Operators 519
41. The Spectral Theorem for Hermitian Operators 523
42. Banach Algebras 533
43. Commutative Banach Algebras 545
44. Banach Algebras with Involutions 557
45. The Spectral Theorem for Normal Operators 567
Notation 573
Appendix: Hilbert Space 575
References 591
Index 597
|
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| bvnumber | BV004808198 |
| classification_rvk | SK 600 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:17:57Z |
| institution | BVB |
| isbn | 0824786432 |
| language | English |
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| physical | XI, 600 S. |
| publishDate | 1992 |
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| publisher | Dekker |
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| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Swartz, Charles 1938- Verfasser (DE-588)131653601 aut An introduction to functional analysis Charles Swartz New York [u.a.] Dekker 1992 XI, 600 S. txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 157 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Pure and applied mathematics 157 (DE-604)BV000001885 157 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002957963&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Swartz, Charles 1938- An introduction to functional analysis Pure and applied mathematics Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4151278-9 |
| title | An introduction to functional analysis |
| title_auth | An introduction to functional analysis |
| title_exact_search | An introduction to functional analysis |
| title_full | An introduction to functional analysis Charles Swartz |
| title_fullStr | An introduction to functional analysis Charles Swartz |
| title_full_unstemmed | An introduction to functional analysis Charles Swartz |
| title_short | An introduction to functional analysis |
| title_sort | an introduction to functional analysis |
| topic | Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Funktionalanalysis Einführung |
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