Some Character Generating Functions on Banach Algebras

2018/08/29 by Rudi Brits, R. Brits, Brits, R. +6 · 1 citation
Computer Science · Mathematics · #Advanced Topics in Algebra #Mathematical and Theoretical Analysis #Matrix Theory and Algorithms #math.FA #msc:15A60 #msc:46H05 #msc:46H10 #msc:46H15 #msc:47B10

paper · pdf · doi:10.48550/arxiv.1808.09952

arxiv created 2018/08/29 · arxiv updated 2018/08/30

Abstract

We consider a multiplicative variation on the classical Kowalski-Słodkowski 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 ϕ:A↦\mathbb C is a continuous function satisfying ϕ(\mathbf 1)=1 and ϕ(x)ϕ(y) ∈ σ(xy) for all x,y∈ A (where σ denotes the spectrum), then ϕ generates a corresponding character ψ_ϕ on A which coincides with ϕ 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, ϕ is always a character.

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• The Multiplicative Kowalski-Slodkowski Theorem for Hermitian Algebras

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