Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 59, No. 1, pp. 111-124 (2002)

Previous Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Multiplication Operators on Weighted Spaces of Continuous Functions

L. Oubbi

Department of Mathematics, Ecole Normale Supérieure de Rabat,
B.P. 5118, Rabat 10105 -- MOROCCO
E-mail: 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.

© 2002 Sociedade Portuguesa de Matemática
© 2002–2007 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition