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Analysis Now

Gert K. Pedersen (Autor)

Buch | Hardcover

280 Seiten

1988 | 1st ed. 1989. Corr. 2nd printing 2001
Springer-Verlag New York Inc.
978-0-387-96788-2 (ISBN)

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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.

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.

Erscheint lt. Verlag	14.11.2001
Reihe/Serie	Graduate Texts in Mathematics ; 118
Zusatzinfo	XIV, 280 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	0-387-96788-5 / 0387967885
ISBN-13	978-0-387-96788-2 / 9780387967882
Zustand	Neuware