Some Character Generating Functions on Banach Algebras
R. Brits, F. Schulz, C. Toure

TL;DR
This paper extends classical character theorems in Banach algebras by exploring functions satisfying spectrum-related multiplicative conditions, especially in $C^*$-algebras and algebras with totally disconnected spectra.
Contribution
It introduces a multiplicative variation of the Kowalski-S extl{}odkowski Theorem, characterizing functions that generate algebra characters under spectral conditions.
Findings
Functions satisfying the spectral multiplicative condition generate characters in $C^*$-algebras.
In algebras with totally disconnected spectra, such functions are always characters.
The results connect spectral properties with algebraic characterizations.
Abstract
We consider a multiplicative variation on the classical Kowalski-S\l{}odkowski Theorem which identifies the characters among the collection of all functionals on a Banach algebra . In particular we show that, if is a -algebra, and if is a continuous function satisfying and for all (where denotes the spectrum), then generates a corresponding character on which coincides with on the principal component of the invertible group of . We also show that, if is any Banach algebra whose elements have totally disconnected spectra, then, under the aforementioned conditions, is always a character.
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Taxonomy
TopicsAdvanced Topics in Algebra · Matrix Theory and Algorithms · Mathematical and Theoretical Analysis
