Holdings: Functional analysis

Functional analysis:

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Bibliographic Details
Main Authors:	Bühler, Theo 1978- (Author), Salamon, Dietmar 1953- (Author)
Format:	Book
Language:	English
Published:	Providence, Rhode Island American Mathematical Society [2018]
Series:	Graduate studies in mathematics 191
Subjects:	Funktionalanalysis Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	xiv, 466 Seiten Diagramme
ISBN:	9781470441906

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MARC


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Record in the Search Index

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adam_text	Contents Preface ix Introduction xi Chapter 1. Foundations 1 §1.1. Metric Spaces and Compact Sets 2 §1.2. Finite-Dimensional Banach Spaces 17 §1.3. The Dual Space 25 §1.4. Hilbert Spaces 31 §1.5. Banach Algebras 35 §1.6. The Baire Category Theorem 40 §1.7. Problems 45 Chapter 2. Principles of Functional Analysis 49 §2.1. Uniform Boundedness 50 §2.2. Open Mappings and Closed Graphs 54 §2.3. Hahn-Banach and Convexity 65 §2.4. Reflexive Banach Spaces 80 §2.5. Problems 101 Chapter 3. The Weak and Weak* Topologies 109 §3.1. Topological Vector Spaces 110 §3.2. The Banach-Alaoglu Theorem 124 §3.3. The Banach-Dieudonne Theorem 130 §3.4. The Eberlein-Smulyan Theorem 134 v VI Contents §3.5. The Kreïn-Milman Theorem §3.6. Ergodic Theory §3.7. Problems Chapter 4. Fredholm Theory §4.1. The Dual Operator §4.2. Compact Operators §4.3. Fredholm Operators §4.4. Composition and Stability §4.5. Problems Chapter 5. Spectral Theory §5.1. Complex Banach Spaces §5.2. Spectrum §5.3. Operators on Hilbert Spaces §5.4. Functional Calculus for Self-Adjoint Operators §5.5. Gelfand Spectrum and Normal Operators §5.6. Spectral Measures §5.7. Cyclic Vectors §5.8. Problems Chapter 6. Unbounded Operators §6.1. Unbounded Operators on Banach Spaces §6.2. The Dual of an Unbounded Operator §6.3. Unbounded Operators on Hilbert Spaces §6.4. Functional Calculus and Spectral Measures §6.5. Problems 140 144 153 163 164 173 179 184 189 197 198 208 222 234 246 261 281 288 295 295 306 313 326 342 Chapter 7. Semigroups of Operators 349 §7.1. Strongly Continuous Semigroups 350 §7.2. The Hille-Yosida-Phillips Theorem 363 §7.3. The Dual Semigroup 377 §7.4. Analytic Semigroups 388 §7.5. Banach Space Valued Measurable Functions 404 §7.6. Inhomogeneous Equations 425 §7.7. Problems 439 Contents vii Appendix A. Zorn and Tychonoff 445 §A.l. The Lemma of Zorn 445 §A.2. Tychonoff’s Theorem 449 Bibliography 453 Notation 459 • Index 461
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spelling	Bühler, Theo 1978- Verfasser (DE-588)1033205508 aut Functional analysis Theo Bühler, Dietmar A. Salamon Providence, Rhode Island American Mathematical Society [2018] © 2018 xiv, 466 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 191 Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Funktionalanalysis (DE-588)4018916-8 s DE-604 Salamon, Dietmar 1953- Verfasser (DE-588)1015895271 aut Graduate studies in mathematics 191 (DE-604)BV009739289 191 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=030323908&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Bühler, Theo 1978- Salamon, Dietmar 1953- Functional analysis Graduate studies in mathematics Funktionalanalysis (DE-588)4018916-8 gnd
subject_GND	(DE-588)4018916-8 (DE-588)4123623-3
title	Functional analysis
title_auth	Functional analysis
title_exact_search	Functional analysis
title_full	Functional analysis Theo Bühler, Dietmar A. Salamon
title_fullStr	Functional analysis Theo Bühler, Dietmar A. Salamon
title_full_unstemmed	Functional analysis Theo Bühler, Dietmar A. Salamon
title_short	Functional analysis
title_sort	functional analysis
topic	Funktionalanalysis (DE-588)4018916-8 gnd
topic_facet	Funktionalanalysis Lehrbuch
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work_keys_str_mv	AT buhlertheo functionalanalysis AT salamondietmar functionalanalysis

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