On the density of CV0(X)⊗A in CV0(X,A)

Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV0(X,A) be the algebra of all weighted vector-valued continuous functions which vanish at infinity with the topology given by the uniform seminorms induced by V. In this paper we present s...

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Bibliographic Details
Published in:	Journal of mathematical analysis and applications Vol. 530; no. 2; p. 127699
Main Authors:	Palacios, Lourdes, Ramos-Martinez, Pavel, Signoret, Carlos
Format:	Journal Article
Language:	English
Published:	Elsevier Inc 15.02.2024
Subjects:	Topological algebras Topological tensor product Vector valued continuous functions spaces Vector valued continuous functions spaces Topological tensor product Topological algebras
ISSN:	0022-247X
Online Access:	Get full text
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Summary:	Let X be a completely regular Hausdorff space and V a Nachbin family on X. For a locally convex algebra A, let CV0(X,A) be the algebra of all weighted vector-valued continuous functions which vanish at infinity with the topology given by the uniform seminorms induced by V. In this paper we present some sufficient conditions under which CV0(X)⊗A is a dense subspace of CV0(X,A) or isomorphic to it.
ISSN:	0022-247X
DOI:	10.1016/j.jmaa.2023.127699