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Cover: 9780387967882 | Analysis Now | Gert K. Pedersen | Buch | Graduate Texts in Mathematics
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Analysis Now
Buch von Gert K. Pedersen
Sprache: Englisch

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Beschreibung
Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view.
Graduate students in mathematics, who want to travel light, will find this book invaluable; impatient young researchers in other fields will enjoy it as an instant reference to the highlights of modern analysis. Starting with general topology, it moves on to normed and seminormed linear spaces. From there it gives an introduction to the general theory of operators on Hilbert space, followed by a detailed exposition of the various forms the spectral theorem may take; from Gelfand theory, via spectral measures, to maximal commutative von Neumann algebras. The book concludes with two supplementary chapters: a concise account of unbounded operators and their spectral theory, and a complete course in measure and integration theory from an advanced point of view.
Inhaltsverzeichnis
1 General Topology.- 1.1. Ordered Sets.- 1.2. Topology.- 1.3. Convergence.- 1.4. Continuity.- 1.5. Separation.- 1.6. Compactness.- 1.7. Local Compactness.- 2 Banach Spaces.- 2.1. Normed Spaces.- 2.2. Category.- 2.3. Dual Spaces.- 2.4. Seminormed Spaces.- 2.5. w*-Compactness.- 3 Hilbert Spaces.- 3.1. Inner Products.- 3.2. Operators on Hilbert Space.- 3.3. Compact Operators.- 3.4. The Trace.- 4 Spectral Theory.- 4.1. Banach Algebras.- 4.2. The Gelfand Transform.- 4.3. Function Algebras.- 4.4. The Spectral Theorem, I.- 4.5. The Spectral Theorem, II.- 4.6. Operator Algebra.- 4.7. Maximal Commutative Algebras.- 5 Unbounded Operators.- 5.1. Domains, Extensions, and Graphs.- 5.2. The Cayley Transform.- 5.3. Unlimited Spectral Theory.- 6 Integration Theory.- 6.1. Radon Integrals.- 6.2. Measurability.- 6.3. Measures.- 6.4. LP-Aspaces.- 6.5. Duality Theory.- 6.6. Product Integrals.- List of Symbols.
Details
Erscheinungsjahr: 1988
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
280 S.
ISBN-13: 9780387967882
ISBN-10: 0387967885
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Pedersen, Gert K.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 22 mm
Von/Mit: Gert K. Pedersen
Erscheinungsdatum: 01.12.1988
Gewicht: 0,617 kg
Artikel-ID: 104859243
Inhaltsverzeichnis
1 General Topology.- 1.1. Ordered Sets.- 1.2. Topology.- 1.3. Convergence.- 1.4. Continuity.- 1.5. Separation.- 1.6. Compactness.- 1.7. Local Compactness.- 2 Banach Spaces.- 2.1. Normed Spaces.- 2.2. Category.- 2.3. Dual Spaces.- 2.4. Seminormed Spaces.- 2.5. w*-Compactness.- 3 Hilbert Spaces.- 3.1. Inner Products.- 3.2. Operators on Hilbert Space.- 3.3. Compact Operators.- 3.4. The Trace.- 4 Spectral Theory.- 4.1. Banach Algebras.- 4.2. The Gelfand Transform.- 4.3. Function Algebras.- 4.4. The Spectral Theorem, I.- 4.5. The Spectral Theorem, II.- 4.6. Operator Algebra.- 4.7. Maximal Commutative Algebras.- 5 Unbounded Operators.- 5.1. Domains, Extensions, and Graphs.- 5.2. The Cayley Transform.- 5.3. Unlimited Spectral Theory.- 6 Integration Theory.- 6.1. Radon Integrals.- 6.2. Measurability.- 6.3. Measures.- 6.4. LP-Aspaces.- 6.5. Duality Theory.- 6.6. Product Integrals.- List of Symbols.
Details
Erscheinungsjahr: 1988
Fachbereich: Analysis
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Reihe: Graduate Texts in Mathematics
Inhalt: xiv
280 S.
ISBN-13: 9780387967882
ISBN-10: 0387967885
Sprache: Englisch
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Pedersen, Gert K.
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 241 x 160 x 22 mm
Von/Mit: Gert K. Pedersen
Erscheinungsdatum: 01.12.1988
Gewicht: 0,617 kg
Artikel-ID: 104859243
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