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## Studia Mathematica

2012 | 210 | 3 | 227-237
Tytuł artykułu

### The Banach algebra of continuous bounded functions with separable support

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Abstrakty
EN
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 C₀(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-Čech compactification of X, is countably compact, and if X is non-separable, is moreover non-normal; in addition C₀(Y) = C₀₀(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 $C_{s}(X)$.
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Tom
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227-237
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wydano
2012
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autor
• Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran
• School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
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