文章基本信息

标题：Multiplication operators on weighted spaces in the non-locally convex framework
本地全文：下载
作者：L. A. Khan ; A. B. Thaheem
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1997
卷号：20
DOI：10.1155/S0161171297000112
出版社：Hindawi Publishing Corporation
摘要：Let X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:X→E is a mapping then define Mψ(f)=ψf (pointwise). The main purpose of this paper is to give necessary and sufficient conditions for Mθ and Mψ to be the multiplication operators on CV0(X,E) where E is a general topological space (or a suitable topological algebra) which is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the assumption that E is locally convex.