Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras

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Cambridge University Press, Mar 25, 1994 - Mathematics - 1616 pages
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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 emphasizes the role of *-algebraic structure and explores the algebraic results that underlie the theory of Banach algebras and *-algebras. The first volume, which contains previously unpublished results, is an independent, self-contained reference on Banach algebra theory.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 of complex algebras rather than topological algebras. Proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, particularly in noncommutative harmonic analysis, and an extensive bibliography. Volume II is forthcoming.

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Introduction to Normed Algebras Examples
The Spectrum
Commutative Algebras and Functional Calculus
Ideals Representations and Radicals
Approximate Identities and Factorization
Automatic Continuity
Structure Spaces
Algebras with Minimal Ideals
Symbol Index

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Page 758 - Functors and categories of Banach spaces. Tensor products, operator ideals and functors on categories of Banach spaces.
Page 721 - On the field of values subordinate to a norm,
Page 722 - FF Bonsall, A minimal property of the norm in some Banach algebras, J.
Page 753 - Concerning the second dual of the group algebra of a locally compact group, J. London Math. Soc. (2), 41 (1990), 445-460. [15] V. LOSERT and H. RINDELER, Assymptotically central functions and invariant extensions of Dirac measures, Proc. Conf. "Probability measures on groups" Oberwollfach, Springer Lecture Notes 1064, 368-378.
Page 717 - The adjoint of a bilinear operation, Proc. Amer. Math. Soc. 2 (1951), 839-848.
Page 764 - Banach spaces of compact multipliers and their dual spaces
Page 738 - Weighted group algebra as an ideal in its second dual space, Proc. Amer. Math Soc.

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