TY - JOUR

T1 - Multiplication Operators on Weighted Spaces of Vector-Valued Continuous Functions

AU - Singh, R. K.

AU - Manhas, JAsbir Singh

PY - 1991

Y1 - 1991

N2 - If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CVQ(X, E) and CVb(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.

AB - If V is a system of weights on a completely regular Hausdorff space X and E is a locally convex space, then CVQ(X, E) and CVb(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.

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U2 - 10.1017/S1446788700032584

DO - 10.1017/S1446788700032584

M3 - Article

AN - SCOPUS:0040061730

VL - 50

SP - 98

EP - 107

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 1

ER -