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Weighted composition operators on nonlocally convex weighted spaces of continuous functions

Весовые композиционные операторы на не локально выпуклых весовых пространствах непрерывных функций

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Abstract

LetV be a system of weights on a completely regular Hausdorff spaceX and letB(E) be the topological vector space of all continuous linear operators on a general topological vector spaceE. LetCV 0(X, E) andCV b (X, E) be the weighted spaces of vector-valued continuous functions (vanishing at infinity or bounded, respectively) which are not necessarily locally convex. In the present paper, we characterize in this general setting the weighted composition operatorsW π,ϕ onCV 0(X, E) (orCV b (X, E)) induced by the operator-valued mappings π:X→B(E) (or the vector-valued mappings π:X→E, whereE is a topological algebra) and the self-map ϕ ofX. Also, we characterize the mappings π:X→B(E) (or π:x→E) and ϕ:X→X which induce the compact weighted composition operators on these weighted spaces of continuous functions.

Abstract

ПустьV—система весов на вполне регулярном хаусдорфовом пространствеX иB(E)—топологическое векторное пространство всех непрерывных линейных операторов на общем топологическом векторном пространствеE. ПустьCV 0(X, E) иCV b (X, E)—весовые пространства векторно-значных непрерывных функций, которые не обязательно являются локально выпуклыми. В работе дается характеризация в этой общей ситуации весовых композиционных операторовW π,ϕ наCV 0(X, E) (CV b (X, E)), порожденных операторно-значными отображениями π:X→B(E) (или вектрно-значными отображениями π:X→E, гдеE—топологическая алгебра) и отображением ф пространстваX на себя. Мы характеризуем также отображенип π:X→B(E) (Или π:X→E) и ф:X→X, которые порождаются компактными весовыми композиционными операторами на эти весовые пространства непрерывных функций.

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  1. Department of Mathematics, University of Jammu, 180 004, Jammu, India

    J. S. Manhas & R. K. Singh

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  1. J. S. Manhas
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Manhas, J.S., Singh, R.K. Weighted composition operators on nonlocally convex weighted spaces of continuous functions. Anal Math 24, 275–292 (1998). https://doi.org/10.1007/BF02771088

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