ACTA UNIVERSITATIS APULENSIS No 19/2009 ON PRECOMPACT MULTIPLICATION OPERATORS ON WEIGHTED FUNCTION SPACES
نویسندگان
چکیده
Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping, consider the induced multiplication operator Mπ : F → F given by Mπ(f)(x) := π(x)f(x), f ∈ G, x ∈ coz(F). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be (1) an equicontinuous operator, (2) a precompact operator and (3) a bounded operator on a subspace F of CVb(X,E) in the non-locally convex setting. 2000 Mathematics Subject Classification: 47B38, 46E40, 46A16
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ACTA UNIVERSITATIS APULENSIS No 18/2009 MULTIPLICATION OPERATORS ON NON-LOCALLY CONVEX WEIGHTED FUNCTION SPACES
Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping and f ∈ F , let Mπ(f)(x) := π(x)f(x). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be a mu...
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