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A reference textbook that summarizes the "algebra of analysis" that includes some mention of the contemporary trends in the development of history. This text provides an up-to-date account of Banach and locally convex algebras with emphasis on general theory, representations and homology. In its description of general theory and in the examples it considers it is faithful to earlier traditions in the subject but differs from those books in being based on an approach through homological algebra. This approach leads Helemskii to consider topics not covered at this level in any other book. These topics include: complemented and uncomplemented ideal; projective and weak tensor products of banach algebras; Taylors multivariable holomorphic functional calculus; the Wedderburn decomposition of Banach algevras; a whole chapter on the homology of Banach algebras.
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.
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.