A Course in Functional Analysis / Edition 2

by John B Conway

Overview

Functional analysis has become a sufficiently large area of mathematics that it is possible to find two research mathematicians, both of whom call themselves functional analysts, who have great difficulty understanding the work of the other. The common thread is the existence of a linear space with a topology or two (or more). Here the paths diverge in the choice of how that topology is defined and in whether to study the geometry of the linear space, or the linear operators on the space, or both. In this book I have tried to follow the common thread rather than any special topic. I have included some topics that a few years ago might have been thought of as specialized but which impress me as interesting and basic. Near the end of this work I gave into my natural temptation and included some operator theory that, though basic for operator theory, might be considered specialized by some functional analysts.

Product Details

ISBN-13:	9780387972459
Publisher:	Springer New York
Publication date:	09/07/1990
Series:	Graduate Texts in Mathematics , #96
Edition description:	2nd ed. 1990
Pages:	400
Product dimensions:	6.14(w) x 9.21(h) x 0.04(d)

Table of Contents

I Hilbert Spaces.- II Operators on Hilbert Space.- III Banach Spaces.- IV Locally Convex Spaces.- V Weak Topologies.- VI Linear Operators on a Banach Space.- VII Banach Algebras and Spectral Theory for Operators on a Banach Space.- VIII C*-Algebras.- IX Normal Operators on Hilbert Space.- X Unbounded Operators.- XI Fredholm Theory.- Appendix A Preliminaries.- §1. Linear Algebra.- §2. Topology.- List of Symbols.

Editorial Reviews

Second Edition

J.B. Conway

A Course in Functional Analysis

"This book is an excellent text for a first graduate course in functional analysis . . . Many interesting and important applications are included . . . This book is a fine piece of work. It includes an abundance of exercises, and is written in the engaging and lucid style which we have come to expect from the author."

—MATHEMATICAL REVIEWS

From the reviews of the second edition:

“This book should be in the library of anyone teaching functional analysis or who wants a working mathematician’s masterfully developed course on functional analysis … . This book is a comprehensive introduction to functional analysis. … I definitely recommend this book to anyone who really want/need to learn true functional analysis for graduate work.” (Philosophy, Religion and Science Book Reviews, bookinspections.wordpress.com, October, 2013)

From the Publisher

Additional exercises, updated references and a rewritten final chapter (Fredholm Theory) distinguish this new edition of a text in which the renowned John Conway undertakes to acquaint graduate students with the most important of the many faces of "functional analysis". He writes with engaging informality (verbal, not mathematical), and has the rare good sense to proceed from the concrete to the abstract, rather than the reverse. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

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