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.
General
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