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＜電子ブック＞
Analysis Now / by Gert K. Pedersen
(Graduate Texts in Mathematics. ISSN:21975612 ; 118)

版	1st ed. 1989.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	1989
本文言語	英語
大きさ	XIV, 280 p : online resource
著者標目	*Pedersen, Gert K author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis FREE:Analysis
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4612-1007-8

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