Operator-valued multiiiiiplication operators on weighted function spaces

• Autorzy: Khan L. A. , Thaheem A. B.
• Języki publikacji: EN

Abstrakty

EN

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, V a Nachbin family of weights on X, and CVb(X,E) the weighted space of continuous JS-valued functions on X. Let B(E) be the vector space of all continuous linear mappings from E into itself, endowed with the topology of uniform convergence on bounded sets. If phi: X -> B(E) is a continuous mapping and f zawiera CVb(X,E), let Mphi,(f) = phif, where (phif)(x) = (phi(x)(f(x) (x zawiera się X). In this paper we give a necessary and sufficient condition for Mphi to be the multiplication operator (i.e. continuous self-mapping) on CVb(X,E), where E is a general space or a locally bounded space. These results extend recent work of Singh and Manhas to a non-locally convex setting and that of the authors where phi has been considered to be a complex or E-valued map.

Słowa kluczowe

EN

Nachbin family of weights; topological vector spaces; weighted topology; multiplication operators

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 599--605
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Khan L. A.

• Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 9028, Jeddah-21413, Saudi Arabia

autor

Thaheem A. B.

• Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Bibliografia

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• [2] L. A. Khan, On approximation in weighted spaces of continuous vector-valued functions, Glasgow Math. J. 29 (1987), 65-68.
• [3] L. A. Khan and A. B. Thaheem, Multiplication operators on weighted spaces in the non-locally convex framework, Internat. J. Math. & Math. Sci. (to appear).
• [4] V. Klee, Shrinkable neighborhoods in Hausdorff linear spaces, Math. Ann. 141 (1960), 281-285.
• [5] L. Nachbin, Weighted approximation for algebras and modules of continuous functions: real and self-adjoint complex cases, Ann. Math. 81 (1965), 289-302.
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• [9] R. K. Singh and J. S. Manhas, Multiplication operators and, dynamical systems, J. Austral. Math. Soc. (Series A) 53 (1992), 92-102; Corrigendum, J. Austral. Math. Soc. (Series A) 58 (1995), 142-142.
• [10] R. K. Singh and W. H. Summers, Composition operators on weighted spaces of continuous functions, J. Austral. Math. Soc. (Series A) 45 (1988), 303-319.
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