Multiplication operators on weighted spaces in the non-locally convex framework

L. A. Khan and A. B. Thaheem

International Journal of Mathematics and Mathematical Sciences, 1997, vol. 20, 1-5

Abstract:

Let X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X , and C V 0 ( X , E ) the weighted space of continuous E -valued functions on X . Let θ : X → C be a mapping, f ∈ C V 0 ( X , E ) and define M θ ( f ) = θ f (pointwise). In case E is a topological algebra, ψ : X → E is a mapping then define M ψ ( f ) = ψ f (pointwise). The main purpose of this paper is to give necessary and sufficient conditions for M θ and M ψ to be the multiplication operators on C V 0 ( 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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:535923

DOI: 10.1155/S0161171297000112

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