Representations of *-Algebras, Locally Compact Groups, and by J. M.G. Fell, R. S. Doran

By J. M.G. Fell, R. S. Doran

This can be an all-encompassing and exhaustive exposition of the speculation of infinite-dimensional Unitary Representations of in the community Compact teams and its generalization to representations of Banach algebras. The presentation is distinctive, available, and self-contained (except for a few user-friendly wisdom in algebra, topology, and summary degree theory). within the later chapters the reader is delivered to the frontiers of present-day wisdom within the zone of Mackey general subgroup analysisand its generalization to the context of Banach *-Algebraic Bundles.

Show description

Read Online or Download Representations of *-Algebras, Locally Compact Groups, and Benach *-Algebraic Bundles, Two Volume Set: Representations of *-Algebras, Locally Compact ... Analysis PDF

Best algebra books

Basic Math & Pre-Algebra For Dummies (2nd Edition)

"Basic Math & Pre-Algebra For Dummies, "2nd version, is an up-to-date and refreshed tackle this center starting place of math schooling. From confident, adverse, and full numbers to fractions, decimals, and percents, readers will construct the mandatory talents to take on extra complex issues, similar to imaginary numbers, variables, and algebraic equations.

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: 12th International Symposium, AAECC-12 Toulouse, France, June 23–27, 1997 Proceedings

This ebook constitutes the strictly refereed complaints of the twelfth foreign Symposium on utilized Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-12, held in Toulouse, France, June 1997. The 27 revised complete papers offered have been rigorously chosen by way of this system committee for inclusion within the quantity.

Additional info for Representations of *-Algebras, Locally Compact Groups, and Benach *-Algebraic Bundles, Two Volume Set: Representations of *-Algebras, Locally Compact ... Analysis

Sample text

Suppose that B has an approximute urzit. For each w E Y 4 3 . 9 0 (e being the unit of G ) let p ( w ) be the multiplier of Be obtained by restricting w t o E,. Then p : We(B)+ W ( E , ) is a *-isomorphism (onto all of %‘-(Be)). Proof. It is obvious that p is a *-homomorphism. The preceding proposition states that it is one-to-one and onto W(B,J. 9. 14). A multiplier u of W will be called unitary if u*u = uu* = 4 and llullo I 1. (a) is a group under the multiplication multipliers of 99 by @(a).

7) To do this, we first notice that, for any bounded linear endomorphism F of A, IlFll = sup{IIF(a)bll:a, b E A, llall I1, llbll 5 1 ) = sup{llbF(a)ll:a,hE A, (8) Ilall 5 1, llhll 5 1). Indeed: Clearly IlFll rnajorizes the two suprema in (8). Now,given E > 0, choose a so that llall = 1 and IIF(a)(l > IlFll - E ; and put b = IIF(u)II-~F(u)*. Then llhll = 1 and IIF(a)bII = IIF(a)JJ> - E. Thus the first supremum in (8) equals (JFII. Similarly the second supremum equals 11Fl1. So (8) is proved. If u = ( A , p ) E %‘-(A),it follows from (8) that 11/41 = suP{IlmbII: Ilall, llbll 5 whence = {Ilal(h)ll: IblL llbll 5 1) = 11~11, I> 780 VIII.

A multiplier u of W will be called unitary if u*u = uu* = 4 and llullo I 1. (a) is a group under the multiplication multipliers of 99 by @(a). operation of W(B), the inverse in @(B) being involution. The map, zO:%(A3) --t G sending each unitary multiplier into its order is a group homomorphism. # of order x-that is, if the group homomorphism no of the last paragraph is onto G. Definition. Let u be a unitary multiplier of A3 of order x. The left action of u is norm-decreasing and its inverse is the norm-decreasing left action of u*.

Download PDF sample

Rated 4.52 of 5 – based on 3 votes