Rocky Mountain Journal of Mathematics

On algebras of Banach algebra-valued bounded continuous functions

Hugo Arizmendi-Peimbert, Angel Carrillo-Hoyo, and Alejandra García-García

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Let $X$ be a completely regular Hausdorff space. We denote by $C(X,A)$ the algebra of all continuous functions on $X$ with values in a complex commutative unital Banach algebra $A$. Let $C_{b}(X,A)$ be its subalgebra consisting of all bounded continuous functions and endowed with the uniform norm. In this paper, we give conditions equivalent to the density of a natural continuous image of $X\times \mathcal {M}(A)$ in the maximal ideal space of $C_{b}(X,A)$.

Article information

Rocky Mountain J. Math., Volume 46, Number 2 (2016), 389-398.

First available in Project Euclid: 26 July 2016

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Zentralblatt MATH identifier

Primary: 46E40: Spaces of vector- and operator-valued functions 46H05: General theory of topological algebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]

Banach algebras vector-valued bounded continuous functions maximal ideal space


Arizmendi-Peimbert, Hugo; Carrillo-Hoyo, Angel; García-García, Alejandra. On algebras of Banach algebra-valued bounded continuous functions. Rocky Mountain J. Math. 46 (2016), no. 2, 389--398. doi:10.1216/RMJ-2016-46-2-389.

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