Multiplication operators and dynamical systems on weighted spaces of cross-sections
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- by R. K. Singh and J. S. Manhas PDF
- Proc. Amer. Math. Soc. 119 (1993), 547-554 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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