Topological Vector Spaces

Intended as a systematic text on topological vector spaces, this text assumes familiarity with the elements of general topology and linear algebra. Similarly, the elementary facts on Hilbert and Banach spaces are not discussed in detail here, since the book is mainly addressed to those readers who wish to go beyond the introductory level. Each of the chapters is preceded by an introduction and followed by exercises, which in turn are devoted to further results and supplements, in particular, to examples and counter-examples, and hints have been given where appropriate. This second edition has been thoroughly revised and includes a new chapter on C^* and W^* algebras.

"The book has firmly established itself both as a superb introduction to the subject and as a very common source of reference. It is beccoming evident that the book itself will only become irrelevant and pale into insignificance when (and if!) the entire subject of topological vector spaces does. An attractive feature of the book is that it is essentially self-contained, and thus perfectly suitable for senior students having a basic training in the area of elementary functional analysis and set-theoretic topology. My view - let even possibly biased for sentimental resasons - is that the book under review would make for a very practical and useful addition to every matahemtaician's personal office collection."Vladimir Pestov in Nesletter of the New Zealand Mathematical Society, August 2000 Second Edition H.H. Schaefer and M.P. Wolff Topological Vector Spaces "The reliable textbook, highly esteemed by several generations of students since its first edition in 1966 . . . The book contains a large number of interesting exercises . . . the book of Schaefer and Wolff is worth reading."—ZENTRALBLATT MATH