Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras
This textbook provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates.Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, i...
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| 245 | 1 | 0 | |a Functional analysis |b an introduction to metric spaces, Hilbert spaces, and Banach algebras |c Joseph Muscat |
| 250 | |a Second edition | ||
| 264 | 1 | |a Cham |b Springer |c [2024] | |
| 300 | |a xiii, 464 Seiten |b Illustrationen |c 235 mm | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 500 | |a 1 Introduction.- Part I: Metric Spaces.- 2 Distance.- 3 Convergence and Continuity.- 4 Completeness and Separability.- 5 Connectedness.- 6 Compactness.- Part II: Banach and Hilbert Spaces.- 7 Normed Spaces.- 8 Continuous Linear Maps.- 9 The Classical Spaces.- 10 Hilbert Spaces.- 11 Banach Spaces.- 12 Differentiation and Integration.- Part III: Banach Algebras.- 13 Banach Algebras.- 14 Spectral Theory.- 15 C*-Algebras | ||
| 520 | |a This textbook provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates.Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, including the spectral theorem, the Gelfand transform, and Banach algebras. Various applications, such as least squares approximation, inverse problems, and Tikhonov regularization, illustrate the theory. Over 1000 worked examples and exercises of varying difficulty present the reader with ample material for reflection.This new edition of Functional Analysis has been completely revised and corrected, with many passages rewritten for clarity, numerous arguments simplified, and a good amount of new material added, including new examples and exercises. The prerequisites, however, remain the same with only knowledge of linear algebra and real analysis of a singlevariable assumed of the reader | ||
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Datensatz im Suchindex
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Contents 1 Introduction. 1.1 Preliminaries. Part I 1 6 Metric Spaces 2 Distance. 2.1 Balls and Open Sets. 2.2 Closed Sets. 15 18 25 3 Convergence and Continuity. 31 31 35 3.1 3.2 4 Completeness and Separability. 4.1 4.2 4.3 5 43 43 55 60 Connected Sets. Components. 63 63 68 Compactness. 6.1 Bounded Sets. 6.2 Totally Bounded Sets. 6.3 Compact Sets. 6.4 The Space C(X, У). 73 73 75 78 86 Part II 7
Completeness. Uniformly Continuous Maps . Separable Spaces. Connectedness . 5.1 5.2 6 Convergence. Continuity . Banach and Hilbert Spaces Normed Spaces. 7.1 Vector Spaces. 7.2 Norms. 99 99 103 xi
Contents xii 7.3 7.4 7.5 Metric and Vector Properties . 112 Complete and Separable Normed Vector Spaces. 117 Series. 120 8 Continuous Linear Maps. 8.1 Operators . 8.2 Operator Norms. 8.3 Isomorphisms and Projections. 8.4 Quotient Spaces. 8.5 R” and Totally Bounded Sets. 127 127 134 141 145 148 9 The Classical Spaces . 9.1 Sequence Spaces . 9.2 Function Spaces. 153 153 172 10 Hilbert Spaces. 10.1 Inner Products. 10.2 Least Squares Approximation. 10.3 Duality H* H
. 10.4 Inverse Problems. 10.5 Orthonormal Bases. 197 197 206 213 220 229 11 Banach Spaces. 11.1 The Open Mapping Theorem. 11.2 Compact Operators. 11.3 The Dual Space X*. 11.4 The Adjoint . . 11.5 Strong and Weak Convergence. 249 249 254 261 270 277 12 Differentiation and Integration. 12.1 Differentiation. 12.2 Integration for Vector-Valued Functions. 12.3 Complex Differentiation and Integration. 293 293 297 304 Part III Banach Algebras 13 Banach Algebras. 13.1 Introduction. 13.2 Power
Series. 13.3 The Group of Invertible Elements. 13.4 Analytic Functions. 315 315 325 333 337 14 Spectral Theory. 14.1 The Spectrum of T. 14.2 The Spectrum of an Operator. 14.3 Spectra of Compact Operators. 14.4 The Functional Calculus. 14.5 The Gelfand Transform. 345 345 350 357 364 370
Contents xiii C*-Algebras. 15.1 Normal Elements. 15.2 Normal Operators in BÇH). 15.3 The Numerical Range. 15.4 The Spectral Theorem for Compact Normal Operators. 15.5 Ideals of Compact Operators . 15.6 Representation Theorems. 15.7 Positive Self-Adjoint Elements. 15.8 Spectral Theorem for Normal Operators. 383 385 391 393 400 407 416 421 431 Hints to Selected Problems. 437 Glossary of Symbols . 451 15 Further Reading. 455 Index. 459 |
| any_adam_object | 1 |
| author | Muscat, Joseph 1967- |
| author_GND | (DE-588)1131715608 |
| author_facet | Muscat, Joseph 1967- |
| author_role | aut |
| author_sort | Muscat, Joseph 1967- |
| author_variant | j m jm |
| building | Verbundindex |
| bvnumber | BV049679186 |
| classification_rvk | SK 600 |
| ctrlnum | (OCoLC)1432549795 (DE-599)BVBBV049679186 |
| discipline | Mathematik |
| edition | Second edition |
| format | Book |
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| id | DE-604.BV049679186 |
| illustrated | Illustrated |
| indexdate | 2025-01-02T15:17:27Z |
| institution | BVB |
| isbn | 9783031275364 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-035022006 |
| oclc_num | 1432549795 |
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| physical | xiii, 464 Seiten Illustrationen 235 mm |
| publishDate | 2024 |
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| publishDateSort | 2024 |
| publisher | Springer |
| record_format | marc |
| spelling | Muscat, Joseph 1967- Verfasser (DE-588)1131715608 aut Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras Joseph Muscat Second edition Cham Springer [2024] xiii, 464 Seiten Illustrationen 235 mm txt rdacontent n rdamedia nc rdacarrier 1 Introduction.- Part I: Metric Spaces.- 2 Distance.- 3 Convergence and Continuity.- 4 Completeness and Separability.- 5 Connectedness.- 6 Compactness.- Part II: Banach and Hilbert Spaces.- 7 Normed Spaces.- 8 Continuous Linear Maps.- 9 The Classical Spaces.- 10 Hilbert Spaces.- 11 Banach Spaces.- 12 Differentiation and Integration.- Part III: Banach Algebras.- 13 Banach Algebras.- 14 Spectral Theory.- 15 C*-Algebras This textbook provides an introduction to functional analysis suitable for lecture courses to final year undergraduates or beginning graduates.Starting from the very basics of metric spaces, the book adopts a self-contained approach to Banach spaces and operator theory that covers the main topics, including the spectral theorem, the Gelfand transform, and Banach algebras. Various applications, such as least squares approximation, inverse problems, and Tikhonov regularization, illustrate the theory. Over 1000 worked examples and exercises of varying difficulty present the reader with ample material for reflection.This new edition of Functional Analysis has been completely revised and corrected, with many passages rewritten for clarity, numerous arguments simplified, and a good amount of new material added, including new examples and exercises. The prerequisites, however, remain the same with only knowledge of linear algebra and real analysis of a singlevariable assumed of the reader bicssc bisacsh Operator theory Functional analysis Banach-Raum (DE-588)4004402-6 gnd rswk-swf Hilbert-Raum (DE-588)4159850-7 gnd rswk-swf Metrischer Raum (DE-588)4169745-5 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Hardcover, Softcover / Mathematik/Analysis Funktionalanalysis (DE-588)4018916-8 s Hilbert-Raum (DE-588)4159850-7 s Banach-Raum (DE-588)4004402-6 s Banach-Algebra (DE-588)4193187-7 s Metrischer Raum (DE-588)4169745-5 s DE-604 Erscheint auch als Online-Ausgabe 978-3-031-27537-1 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=035022006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Muscat, Joseph 1967- Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras bicssc bisacsh Operator theory Functional analysis Banach-Raum (DE-588)4004402-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Metrischer Raum (DE-588)4169745-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4159850-7 (DE-588)4169745-5 (DE-588)4018916-8 (DE-588)4193187-7 |
| title | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras |
| title_auth | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras |
| title_exact_search | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras |
| title_full | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras Joseph Muscat |
| title_fullStr | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras Joseph Muscat |
| title_full_unstemmed | Functional analysis an introduction to metric spaces, Hilbert spaces, and Banach algebras Joseph Muscat |
| title_short | Functional analysis |
| title_sort | functional analysis an introduction to metric spaces hilbert spaces and banach algebras |
| title_sub | an introduction to metric spaces, Hilbert spaces, and Banach algebras |
| topic | bicssc bisacsh Operator theory Functional analysis Banach-Raum (DE-588)4004402-6 gnd Hilbert-Raum (DE-588)4159850-7 gnd Metrischer Raum (DE-588)4169745-5 gnd Funktionalanalysis (DE-588)4018916-8 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | bicssc bisacsh Operator theory Functional analysis Banach-Raum Hilbert-Raum Metrischer Raum Funktionalanalysis Banach-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=035022006&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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