Analysis Now / Edition 1

by Gert K. Pedersen

Overview

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.

Product Details

ISBN-13:	9781461269816
Publisher:	Springer New York
Publication date:	09/30/2012
Series:	Graduate Texts in Mathematics , #118
Edition description:	Softcover reprint of the original 1st ed. 1989
Pages:	280
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.

Editorial Reviews

G.K. Pedersen

Analysis Now

"The writing is clear and precise, but has an informal and humorous touch which enlivens the material. One of the strengths of the book is the excellent set of problems, which accompany the text."—MATHEMATICAL REVIEWS

From the Publisher

Nicely produced text for graduate students, derived from a course on the "fundamentals of functional analysis" given at the University of Copenhagen in 1982/83, and intended to provide review of "what every young analyst should know". The six chapters treat general topology, Banach spaces, Hilbert spaces, spectral theory, unbounded operators, integration theory. Discussion of conceptual/methodological material is brief and to the point, and much space is given to the exercises. Useful contribution to the advanced pedagogical literature. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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