Some character generating functions on Banach algebras

[摘要] We consider a multiplicative variation on the classical Kowalski-Slodkowski Theorem which identifies the characters among the collection of all functionals on a Banach algebra A. In particular we show that, if A is a C*-algebra, and if phi : A bar right arrow C is a continuous function satisfying phi(1) = 1 and phi(x)phi(y) is an element of sigma(xy) for all x, y is an element of A (where sigma denotes the spectrum), then phi generates a corresponding character psi(phi) on A which coincides with phi on the principal component of the invertible group of A. We also show that, if A is any Banach algebra whose elements have totally disconnected spectra, then, under the aforementioned conditions, phi is always a character. (C) 2018 Elsevier Inc. All rights reserved.

[发布日期] 2018-12-15

[关键词] Banach algebra;Spectrum;Character;Linear functional