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Operators and Dynamical Systems on Weighted Function Spaces

✍ Scribed by R. K. Singh; J. S. Manhas

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
360 KB
Volume
169
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let E be a locally convex Hausdorff space. Let CV~0~(X, E) and CV~b~(X, E) be the weighted locally convex spaces of vector‐valued continuous functions with a topology generated by seminorms which are weighted analogue of the supremum norm. In the present paper, we characterize multiplication operators and weighted composition operators on the spaces CV~0~(X, E) and CV~b~(X, E) induced by scalar‐valued and vector‐valued mappings. A (linear) dynamical system on these weighted spaces is obtained as an application of the theory of multiplication operators.

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