This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far one can go beyond the classical framework of Banach algebras while still retaining substantial results.The need for such an extension of the standard theory of normed algebras has been apparent since the early days of the theory of topological algebras, most notably the locally convex ones. It is worth noticing that the previous demand was due not only to theoretical reasons, but also to potential concrete applications of the new discipline.View full description
- Published: April 1986
- Imprint: NORTH-HOLLAND
- ISBN: 978-0-444-87966-0
Table of ContentsPart I: General Theory. General Concepts. Spectrum (Local Theory). Projective Limit Algebras. Inductive Limit Algebras. Spectrum (Global Theory). The Gel'fand Map. Spectra of Certain Particular Topological Algebras. Some Special Classes of Topological Algebras. Structure Theory. Part II: Topological Tensor Products. Topological Tensor Products of Topological Algebras. Topological Tensor Product Algebras. Examples. Spectra of Topological Tensor Product Algebras. Properties of Permanence of Topological Tensor Product Algebras. Generalized Spectra in the Presence of Approximate Identities. Representation Theory. Topological Algebras with Involution. Representation Theory (continued). Bibliography. Index.