Weighted Composition Operators on Non-Locally Convex Weighted Spaces

Abstract

Let (A, τ ) be a topological vector space, X and Y Hausdorff completely regular spaces and V and U Nachbin families on X and Y respectively. For a pair of maps ϕ : Y → X and ψ : Y → L(A), L(A) being the vector space of continuous operators from A into itself, we study the conditions under which the corresponding weighted composition operator ψC ϕ , assigning to each f ∈ CV (X, A) the function y → ψ y (f • ϕ(y)), maps a subspace E of CV (X, A) continuously into another given subspace F of CU(Y, A). We also examine when ψC ϕ is bounded, (locally) equicontinuous or (locally) precompact from E into F .

Mean Ergodic Multiplication Operators on Weighted Spaces of Continuous Functions

“…Multiplication operators on weighted spaces of (vector valued) continuous functions have been investigated by Manhas [13], [14], Singh and Manhas [15], [19], [21], Oubbi [17], [18] and Klilou and Oubbi [9] among others. See also the book by Singh and Manhas [20].…”

Ergodic properties of operators on spaces of functions

“…Multiplication operators on weighted spaces of (vector valued) continuous functions have been investigated by Manhas [59], [60], Singh and Manhas [61], [77], [79], Oubbi [67], [68] and Klilou and Oubbi [50] among others. See also the book by Singh and Manhas [78].…”