PORTUGALIAE MATHEMATICA Vol. 59, No. 1, pp. 111124 (2002) 

Multiplication Operators on Weighted Spaces of Continuous FunctionsL. OubbiDepartment of Mathematics, Ecole Normale Supérieure de Rabat,B.P. 5118, Rabat 10105  MOROCCO Email: l_oubbi@hotmail.com Abstract: Let $V$ be a Nachbin family on the Hausdorff completely regular space $X$, $E$ a locally convex space, ${\cal B}(E)$ the algebra of all continuous operators on $E$ and $\psi:X\to{\cal B}(E)$ a map. We give necessary and sufficient conditions for the induced linear mapping $M_\psi: f\mapsto\psi(\ )(f(\ ))$ to be a multiplication operator on a subspace of the weighted space of $E$valued continuous functions $CV(X, E)$. Next, we characterize the bounded multiplication operators and show that, at least whenever $X$ is a $V_{\R}$space, such an operator is precompact if and only if it is trivial. Keywords: multiplication operator; Nachbin family; weighted space. Classification (MSC2000): 47B38, 46E10, 46E25. Full text of the article:
Electronic version published on: 9 Feb 2006. This page was last modified: 27 Nov 2007.
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