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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Vydáno v:Journal of mathematical analysis and applications Ročník 530; číslo 2; s. 127699
Hlavní autoři: Palacios, Lourdes, Ramos-Martinez, Pavel, Signoret, Carlos
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 15.02.2024
Témata:
Topological algebras
Topological tensor product
Vector valued continuous functions spaces
Vector valued continuous functions spaces
Topological tensor product
Topological algebras
ISSN:0022-247X
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Shrnutí: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