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Multiplication operators and dynamical systems on weighted spaces of cross-sections

Authors: R. K. Singh and J. S. Manhas
Journal: Proc. Amer. Math. Soc. 119 (1993), 547-554
MSC: Primary 47B37; Secondary 54H20
MathSciNet review: 1155602
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Abstract: Let $ Y$ be a Hausdorff topological space, let $ V$ be a system of weights on $ Y$, and let $ L{V_0}(Y)$ and $ L{V_b}(Y)$ be the weighted locally convex spaces of cross-sections with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper, we characterise the multiplication operators on the spaces $ L{V_0}(Y)$ and $ L{V_b}(Y)$ induced by the scalar-valued, the vector-valued, and the operator-valued mappings. A (linear) dynamical system on the weighted spaces of cross-sections is obtained as an application of the theory of the multiplication operators. Many examples are given to illustrate the theory.

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Keywords: Weights, cross-sections, seminorms, vector-valued and operator-valued mappings, multiplication operators, dynamical systems
Article copyright: © Copyright 1993 American Mathematical Society