A Characterization of Coherence of the Algebra of Bounded Uniformly Continuous Functions on a Metric Space and the Spectrum of General Self-Adjoint Banach Function Algebras

Autor: Raymond Mortini, Rudolf Rupp
Rok vydání: 2021
Předmět:
Zdroj: Results in Mathematics. 76
ISSN: 1420-9012
1422-6383
DOI: 10.1007/s00025-021-01523-1
Popis: It is shown that the Banach algebra $$C_{ub}(X,d)$$ of bounded uniformly $${{\mathbb {K}}}$$ -valued continuous functions on a metric space (X, d) is coherent if and only if d is a uniformly discrete metric, or equivalently, if X does not contain twin sequences. The proof is based on Neville’s result that $$C(X, {\mathbb {R}})$$ for a Tychonov space is coherent if and only if X is basically disconnected. Since $$C_{ub}(X,d)$$ is self-adjoint, we also include in the survey part some general results on the spectrum M(A) of general self-adjoint Banach function algebras which we need for the special case here.
Databáze: OpenAIRE
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