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- W2057360023 abstract "We prove a commutative Gelfand--Naimark type theorem, by showing that the set $C_s(X)$ of continuous bounded (real or complex valued) functions with separable support on a locally separable metrizable space $X$ (provided with the supremum norm) is a Banach algebra, isometrically isomorphic to $C_0(Y)$, for some unique (up to homeomorphism) locally compact Hausdorff space $Y$. The space $Y$, which we explicitly construct as a subspace of the Stone--v{C}ech compactification of $X$, is countably compact, and if $X$ is non-separable, is moreover non-normal; in addition $C_0(Y)=C_{00}(Y)$. When the underlying field of scalars is the complex numbers, the space $Y$ coincides with the spectrum of the ${C}^*$-algebra $C_s(X)$. Further, we find the dimension of the algebra $C_s(X)$." @default.
- W2057360023 created "2016-06-24" @default.
- W2057360023 creator A5054770765 @default.
- W2057360023 date "2012-05-12" @default.
- W2057360023 modified "2023-09-25" @default.
- W2057360023 title "The Banach algebra of continuous bounded functions with separable support" @default.
- W2057360023 cites W1581053030 @default.
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- W2057360023 doi "https://doi.org/10.48550/arxiv.1205.2802" @default.
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