Essential Results of Functional Analysis

Zimmer, Robert J.

ISBN 10: 0226983382 / ISBN 13: 9780226983387

Published by University of Chicago Press, 1990

Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. Seller Inventory # G0226983382I3N00

Synopsis:

Functional analysis is a broad mathematical area with strong connections to many domains within mathematics and physics. This book, based on a first-year graduate course taught by Robert J. Zimmer at the University of Chicago, is a complete, concise presentation of fundamental ideas and theorems of functional analysis. It introduces essential notions and results from many areas of mathematics to which functional analysis makes important contributions, and it demonstrates the unity of perspective and technique made possible by the functional analytic approach.

Zimmer provides an introductory chapter summarizing measure theory and the elementary theory of Banach and Hilbert spaces, followed by a discussion of various examples of topological vector spaces, seminorms defining them, and natural classes of linear operators. He then presents basic results for a wide range of topics: convexity and fixed point theorems, compact operators, compact groups and their representations, spectral theory of bounded operators, ergodic theory, commutative C*-algebras, Fourier transforms, Sobolev embedding theorems, distributions, and elliptic differential operators. In treating all of these topics, Zimmer's emphasis is not on the development of all related machinery or on encyclopedic coverage but rather on the direct, complete presentation of central theorems and the structural framework and examples needed to understand them. Sets of exercises are included at the end of each chapter.

For graduate students and researchers in mathematics who have mastered elementary analysis, this book is an entrée and reference to the full range of theory and applications in which functional analysis plays a part. For physics students and researchers interested in these topics, the lectures supply a thorough mathematical grounding.

About the Author: Robert J. Zimmer (1947-2023) was president of the University of Chicago. He is the author of Ergodic Theory and Semisimple Groups and Essential Results of Functional Analysis and coauthor of Ergodic Theory, Groups, and Geometry. He is also the author of more than eighty mathematical research articles.

Bibliographic Details

Title: Essential Results of Functional Analysis
Publisher: University of Chicago Press
Publication Date: 1990
Binding: Paperback
Condition: Good
Dust Jacket Condition: No Jacket