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Introduction to functional analysis. 2nd ed. (Reprint of the orig. 1980, publ. by John Wiley & Sons, Inc., New York etc.). (English) Zbl 0654.46002
Malabar, Florida: Robert E. Krieger Publishing Company. XI, 467 p.; $ 42.50 (1986).
Since the first edition of this book (1958; Zbl 0081.102) a lot of textbooks on functional analysis appeared, but the book under review ist still one of the best of them. To make the book even more accessible to the student of our days, some changes have been made. Background material (on topology and integration) is omitted, because it belongs to the standard curriculum of today. On the other hand, a lot of new material is added, on weak topologies and duality, on equicontinuity, on Fredholm operators, and a whole chapter on Banach algebras. Moreover, the number of problems in the text has increased considerably.
It is of great value, that this beautiful textbook is now again available.
Reviewer: J.Lorenz

MSC:
46-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to functional analysis
47-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory
46B03 Isomorphic theory (including renorming) of Banach spaces
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
46H05 General theory of topological algebras
46B10 Duality and reflexivity in normed linear and Banach spaces
46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
47A10 Spectrum, resolvent
47A53 (Semi-) Fredholm operators; index theories
47A60 Functional calculus for linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)