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Functional analysis / Dzung Minh Ha.

By: Ha, Dzung Minh.
Material type: materialTypeLabelBookPublisher: Ithaca, NY : Matrix Editions, c2006Description: v. <1- > : ill. ; 25 cm. + hbk.ISBN: 0971576610 ; 9780971576612.Subject(s): Functional analysisDDC classification: 515.7
Contents:
v. 1. A gentle introduction. Three important inequalities -- Metric and topological spaces -- Normed spaces -- Operators on normed spaces -- Inner product spaces -- The Banach space C(X) -- Additional topics.
Summary: Covers metric, topological, normed, and Hilbert spaces; bounded linear operators; Hamel, Schauder, and Hilbert bases. Theorems include Banach fixed point, Baire's category, Banach-Steinhaus, open mapping, Weierstrass approximation, Stone-Weierstrass, Baire-Osgood, Muntz. Appendix gives background on set theory and linear algebra. Index and appoximately 120 pages of solutions to odd-numbered exercises--Provided by publisher.

Enhanced descriptions from Syndetics:

"Covers metric, topological, normed, and Hilbert spaces; bounded linear operators; Hamel, Schauder, and Hilbert bases. Theorems include Banach fixed point, Baire's category, Banach-Steinhaus, open mapping, Weierstrass approximation, Stone-Weierstrass, Baire-Osgood, Muntz. Appendix gives background on set theory and linear algebra. Index and appoximately 120 pages of solutions to odd-numbered exercises"--Provided by publisher.

Bibliography: (pages 618-621) and index.

v. 1. A gentle introduction.
Three important inequalities -- Metric and topological spaces -- Normed spaces -- Operators on normed spaces -- Inner product spaces -- The Banach space C(X) -- Additional topics.

Covers metric, topological, normed, and Hilbert spaces; bounded linear operators; Hamel, Schauder, and Hilbert bases. Theorems include Banach fixed point, Baire's category, Banach-Steinhaus, open mapping, Weierstrass approximation, Stone-Weierstrass, Baire-Osgood, Muntz. Appendix gives background on set theory and linear algebra. Index and appoximately 120 pages of solutions to odd-numbered exercises--Provided by publisher.

Reviews provided by Syndetics

CHOICE Review

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. ^BSumming Up: Highly recommended. Upper-division undergraduates; graduate students. F. E. J. Linton emeritus, Wesleyan University
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