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

DOI:
https://doi.org/10.1090/S0002-9939-1993-1155602-0

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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*Operators and dynamical systems on weighted function spaces*, preprint.

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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