If V is a system of weights on a completely regular Hausdorff space X and £ is a locally convex space, then CV 0 (X, E) and CV b (X, E) are locally convex spaces of vector-valued continuous functions with topologies generated by seminorms which are weighted analogues of the supremum norm. In this paper we characterise multiplication operators on these spaces induced by scalar-valued and vector-valued mappings. Many examples are presented to illustrate the theory.
Let X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CV b (X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CV b (X, T) induced by operator-valued mappings and then obtain a (linear) dynamical system on this weighted function space.1991 Mathematics subject classification (Amer. Math. Soc.): 34 C 35, 46 E 40, 47 B 38.
Let H (D) be the space of analytic functions on the unit disc D. Let ϕ be an analytic self-map of D and ψ 1 ,ψ 2 ∈ H (D). Let C ϕ , M ψ and D denote the composition, multiplication and differentiation operators, respectively. In order to treat the products of these operators in a unified manner, Stević et al. introduced the following operator
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