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On algebras of bounded continuous functions valued in a topological algebra

Arizmendi-Peimbert H., Chō M., Garcia A.

Commentationes Mathematicae

2017

Vol 57, No. 2

123--129

Let X be a completely regular space. We denote by C(X,A) the locally convex algebra of all continuous functions on X valued in a locally convex algebra A with a unit e. Let Cb(X,A) be its subalgebra consisting of all bounded continuous functions and endowed with the topology given by the uniform seminorms of A on X. It is clear that A can be seen as the subalgebra of the constant functions of Cb(X,A). We prove that if A is a Q-algebra, that is, if the set G(A) of the invertible elements of A is open, or a Q-álgebra with a stronger topology, then the same is true for Cb(X,A).