Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-27T06:34:30.293Z Has data issue: false hasContentIssue false
  • English
  • Français

Multiplication Operators and Dynamical Systems

Part of: Linear function spaces and their duals Special classes of linear operators

Published online by Cambridge University Press:  09 April 2009

R. K. Singh  and
Jasbir Singh Manhas
R. K. Singh
Affiliation:
University of JammuJammu-180004, India
Jasbir Singh Manhas
Affiliation:
University of JammuJammu-180004, India
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let X be a completely regular Hausdorff space, let V be a system of weights on X and let T be a locally convex Hausdorff topological vector space. Then CVb(X, T) is a locally convex space of vector-valued continuous functions with a topology generated by seminorms which are weighted analogues of the supremum norm. In the present paper we characterize multiplication operators on the space CVb(X, T) induced by operator-valued mappings and then obtain a (linear) dynamical system on this weighted function space.

Keywords

system of weightslocally convex spacesmultiplication operatorsdynamical systems.

MSC classification

Secondary: 46E40: Spaces of vector- and operator-valued functions 47B38: Operators on function spaces (general)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 92 - 102
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Bierstedt, K. D., ‘Gewichtete Raume Stetiger Vektorwertiger Funktionen und das Injektive Tensor-produkt I’, J. reine u. angew Math. 259 (1973), 186–210.Google Scholar
[2]Bierstedt, K. D., ‘Gewichtete Reume Stetiger Vektorwertiger Funktionen und das Injektive Tensor-produkt II’, J. reine u. angew Math. 260 (1973), 133–146.Google Scholar
[3]Chernoff, P. and Marsden, J., ‘On continuity and smoothness of group actions’, Bull. Amer. Math. Soc. 76 (1970), 1044–1049.CrossRefGoogle Scholar
[4]Gronthedieck, A., Topological Vector Spaces, (Gordon and Breach, New York, 1975).Google Scholar
[5]Kothe, G., Topological Vector Spaces I (Springer-Verlag, Berlin, 1969).Google Scholar
[6]Nachbin, L., Elements of Approximation Theory, Math. Studies 14, (Van Nostrand, Princeton, 1967).Google Scholar
[7]Prolla, J. B., ‘Weighted spaces of vector-valued continuous functions’, Ann. Mat. Pura. Appl. 89 (1971), 145–158.CrossRefGoogle Scholar
[8]Singh, R. K. and Manhas, Jasbir Singh, ‘Multiplication operators on spaces of vectorvalued continuous functions’, J. Austral. Math. Soc. (Series A), 50 (1991), 98–107.CrossRefGoogle Scholar
[9]Singh, R. K. and Summers, W. H., ‘Composition operators on weighted spaces of continuous functions’, J. Austral. Math. Soc. (Series A) 45 (1988), 303–319.CrossRefGoogle Scholar
[10]Summers, W. H., Weighted locally convex spaces of continuous functions, Ph.D. Dissertation, Louisiana State University, 1968.Google Scholar