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http://dx.doi.org/10.4134/CKMS.c170090

WEIGHTED COMPOSITION OPERATORS ON NACHBIN SPACES WITH OPERATOR-VALUED WEIGHTS  

Klilou, Mohammed (Department of Mathematics Team GrAAF, Laboratory LMSA, Center CeReMAR Faculty of Sciences, Mohammed V University in Rabat)
Oubbi, Lahbib (Department of Mathematics Team GrAAF, Laboratory LMSA, Center CeReMAR Ecole Normale Superieure, Mohammed V University in Rabat)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.4, 2018 , pp. 1125-1140 More about this Journal
Abstract
Let A be a normed space, ${\mathcal{B}}(A)$ the algebra of all bounded operators on A, and V a family of strongly upper semicontinuous functions from a Hausdorff completely regular space X into ${\mathcal{B}}(A)$. In this paper, we investigate some properties of the weighted spaces CV (X, A) of all A-valued continuous functions f on X such that the mapping $x{\mapsto}v(x)(f(x))$ is bounded on X, for every $v{\in}V$, endowed with the topology generated by the seminorms ${\parallel}f{\parallel}v={\sup}\{{\parallel}v(x)(f(x)){\parallel},\;x{\in}X\}$. Our main purpose is to characterize continuous, bounded, and locally equicontinuous weighted composition operators between such spaces.
Keywords
generalized Nachbin family; generalized weighted spaces of vector-valued continuous functions; weighted composition operators; multiplication operators;
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