Download PDF by Theodore W. Palmer: Banach Algebras and the General Theory of *-Algebras: Volume

By Theodore W. Palmer

ISBN-10: 0521366372

ISBN-13: 9780521366373

This is often the 1st quantity of a quantity set that gives a contemporary account of simple Banach algebra thought together with all recognized effects on normal Banach *-algebras. This account emphasizes the position of *-algebraic constitution and explores the algebraic effects that underlie the speculation of Banach algebras and *-algebras. the 1st quantity, which incorporates formerly unpublished effects, is an autonomous, self-contained reference on Banach algebra concept. every one subject is handled within the greatest fascinating generality in the framework of a few classification of advanced algebras instead of topological algebras. Proofs are provided in whole aspect at a degree obtainable to graduate scholars. The booklet incorporates a wealth of historic reviews, history fabric, examples, really in noncommutative harmonic research, and an in depth bibliography. quantity II is imminent.

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Additional info for Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras (Encyclopedia of Mathematics and its Applications)

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3(c) shows that when the annihilator ideal is zero, the set o f multipliers is simply the center of the double centralizer algebra. Multipliers were defined by Helgason [1956] and first systematically studied on commutative Banach algebras (with annihilator ideal { 0 } ) by Ju-kwei Wang in his thesis [1961]. They are still most often considered in this context. The standard reference for their theory is Ronald Larsen [1971]. However, we are aware o f a number of papers which purport to use multipliers on noncommutative algebras but apply properties which hold only in the commutative case.

B. ) In a direct product, any element 6 of B can be identified with the pair (n (b), ip(b)) and thus B is isomorphic to the Cartesian product, A x C with pointwise operations. This Cartesian product algebra can be given the /x -norm I! (a, c) || = max{||a||, ||c||} V a € A; c e C which makes the isomorphism into a homeomorphic isomorphism. The images o f A and C in B are both closed ideals, and another way to describe a direct product is to say that it is the sum of two closed ideals with intersection { 0 }.

In a semidirect product, each element 6 is the sum of 6 — \ ° ip(b) and X°ip(b), where the first summand is in the image o f

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Banach Algebras and the General Theory of *-Algebras: Volume 1, Algebras and Banach Algebras (Encyclopedia of Mathematics and its Applications) by Theodore W. Palmer


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