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Review from Choice Magazine

Functional Analysis
Volume 1: A Gentle Introduction

 

Choice: Current Reviews for Academic Libraries is published by the American Library Association. A reader survey ranked it "the best short critical evaluations of new titles available anywhere" .

The following review appeared in the March 2007 issue.   


"This first volume in a projected three-volume set on functional analysis calls nothing more to mind than the massive first volume of the classic 1960s-era series by Nelson Dunford and Jacob T. Schwartz, Linear
Operators (3 v., 1967-71). Where the latter was a terse, exhaustive encyclopedic compendium of all there was to know on the subject, however, the present volume sets out instead to offer a thorough, deliberately slow textbook presentation of all the standard topics any introductory functional analysis course might wish to cover, along with a multitude of instructive examples and, more importantly, counterexamples. 

Numerous exercises appear after each section, and a long appendix (exceeding 100 pages) presents detailed solutions to a good half of them. Author Ha largely succeeds in his stated aim "to write a textbook that I would like to have studied from as a student."

Multiple appendixes (the rest including prerequisites from set theory and linear algebra), along with a nice bibliography, list of notations, and thorough index bring up the rear of this highly accessible, self-contained work. Summing Up: Highly recommended. 

Upper-division undergraduates; graduate students." F. E. J. Linton, emeritus, Wesleyan University    

Reprinted with permission from  Choice . Copyright by the American Library Association