Multiplication operators on weighted spaces of vector-valued continuous functions

Abstract

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.

Multiplication Operators and Dynamical Systems

“…This paper is a continuation of our earlier paper [8] in which we have studied multiplication operators on weighted spaces of vector-valued con- [2] Multiplication Operators and Dynamical Systems 93 tinuous functions induced by scalar-valued and vector-valued mappings. In the present paper we concentrate on the study of multiplication operators on weighted spaces of vector-valued mappings induced by operator-valued mappings and then we endeavor to study a (linear) dynamical system on these function spaces.…”

Multiplication operators on weighted spaces in the non‐locally convex framework

“…Since then it has been studied extensively for a variety of problems such as weighted approximation, characterization of the dual space, approximation property, description of inductive limit and of tensor-product, etc for both scalar-and vector-valued functions (for instance see [1][2][3][4][5][8][9][10][11][12][13][14]). Recently Singh and Summers [13] have studied the notion of composition operators on CVo(X, C).…”

“…Recently Singh and Summers [13] have studied the notion of composition operators on CVo(X, C). Later, Singh and Manhas [12] made an analogous study of multiplication operators on CVo(X, E), assuming E to be a locally convex space or a locally m-convex algebra. The purpose of this paper is to generalize the results of Singh and Manhas [12] space We mention that if V S (X), then CV(X, E) CVo(X, E) C(X, E) and w , the stricl topology and write as (C(X, E), ); if V S + (X), then CV(X, E) CVo(X, E) C(X, E) and w k, the compact-open topology and we write as (C(X, E), k).…”

“…Later, Singh and Manhas [12] made an analogous study of multiplication operators on CVo(X, E), assuming E to be a locally convex space or a locally m-convex algebra. The purpose of this paper is to generalize the results of Singh and Manhas [12] space We mention that if V S (X), then CV(X, E) CVo(X, E) C(X, E) and w , the stricl topology and write as (C(X, E), ); if V S + (X), then CV(X, E) CVo(X, E) C(X, E) and w k, the compact-open topology and we write as (C(X, E), k). For more information on weighted spaces, we refer to 1-2,9-14] when E is a scalar field or a locally convex space and to [1,[3][4][5]8] in the general setting.…”

Multiplication Operators and Dynamical Systems on Weighted Spaces of Cross-Sections

“…We initiated the study of these operators on the weighted function spaces in [7]. This paper is a continuation of our earlier papers [8,9] in which we studied the multiplication operators on the weighted spaces of vector-valued functions.…”