The present book is intended to be a systematic text on topological vector spaces and presupposes familiarity with the elements of general topology and linear algebra. The author has found it unnecessary to rederive these results, since they are equally basic for many other areas of mathematics, and every beginning graduate student is likely to have made their acquaintance. Simi- larly, the elementary facts on Hilbert and Banach spaces are widely known and are not discussed in detail in this book, which is: plainly addressed to those readers who have attained and wish to get beyond the...

Vector lattices-also called Riesz spaces, K-lineals, or linear lattices-were first considered by F. Riesz, L. Kantorovic, and H. Freudenthal in the middle nineteen thirties; thus their early theory dates back almost as far as the beginning of the systematic investigation of Banach spaces. Schools of research on vector lattices were subsequently founded in the Soviet Union (Kantorovic, Judin, Pinsker, Vulikh) and in Japan (Nakano, Ogasawara, Yosida); other important contri- butions came from the United States (G. Birkhoff, Kakutani, M. H. Stone). L. Kantorovic and his school first recognized...

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...