Banach And Locally Convex Algebras (oxford Mathematical Monographs)

This text provides an up-to-date account of Banach and locally convex algebras with a particular emphasis on general theory, representations, and homology. In his descriptions and examples of general theory, the author remains aware of traditional trends in the field analysis while breaking from convention in his approach to "the algebra of analysis" through homological algebra. Such an approach allows Helemskii to consider topics not covered at this level in any other book, including complemented and uncomplemented ideals, projective and weak tensor products of banach algebras, Taylor's multivariable holomorphic functional calculus, the Wedderburn decomposition of Banach algebras, and the homology of Banach algebras. Graduate students and researchers in Banach algebras are sure to find this an invaluable volume. Content: Chapter 0. Foundations Chapter I. Initial concepts and first results Chapter II. Around the spectrum Chapter III. Basic stock of examples Chapter IV. Commutative and star Banach algebras Chapter V. Polynormed algebras that are near to Banach algebras Chapter VI. Modules, they are also representations Chapter VII. Problems leading to homology and the elements of homology theory Bibliography Index Index of notation This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. This approach leads Helemskii to consider topics not covered at this level in any other book.