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This is the first volume of a two volume set that provides a modern account of basic Banach algebra theory including all known results on general Banach *-algebras. This account emphasises the role of *-algebra structure and explores the algebraic results which underlie the theory of Banach algebras and *-algebras. This first volume is an independent, self-contained reference on Banach algebra theory. Each topic is treated in the maximum interesting generality within the framework of some class complex algebras rather than topological algebras. In both volumes proofs are presented in complete detail at a level accessible to graduate students. In addition, the books contain a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Together these books will become the standard reference for the general theory of *-algebras.
Operator theory --- Banach algebras --- Banach algebras. --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces --- Topological algebras --- Algebres de banach --- Algebres topologiques --- C star algebres
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Geometry, Algebraic --- Noncommutative rings --- 512.73 --- 517.986 --- Non-commutative rings --- Associative rings --- Algebraic geometry --- Geometry --- Cohomology theory of algebraic varieties and schemes --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- 512.73 Cohomology theory of algebraic varieties and schemes --- Noncommutative rings. --- Géométrie algébrique --- Anneaux non commutatifs --- Géométrie algébrique --- Geometry, Algebraic. --- Géométrie différentielle non commutative --- Géométrie différentielle non commutative --- C etoile-algebres
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