Multiplication operators on weighted spaces in the non-locally convex framework
Let X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:X→E is a m...
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| Format: | Article |
| Language: | English |
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Wiley
1997-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171297000112 |
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| author | L. A. Khan A. B. Thaheem |
| author_facet | L. A. Khan A. B. Thaheem |
| author_sort | L. A. Khan |
| collection | DOAJ |
| description | Let X be a completely regular Hausdorff space, E a topological vector space, V a
Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions
on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is
a topological algebra, ψ:X→E is a mapping then define Mψ(f)=ψf (pointwise). The main purpose
of this paper is to give necessary and sufficient conditions for Mθ and Mψ to be the multiplication
operators on CV0(X,E) where E is a general topological space (or a suitable topological algebra) which
is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the
assumption that E is locally convex. |
| format | Article |
| id | doaj-art-48cbccce56974b809d10c158fef1e0f9 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1997-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-48cbccce56974b809d10c158fef1e0f92025-02-03T01:04:16ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251997-01-01201757910.1155/S0161171297000112Multiplication operators on weighted spaces in the non-locally convex frameworkL. A. Khan0A. B. Thaheem1Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Mail Box 469, Dhahran 31261, Saudi ArabiaLet X be a completely regular Hausdorff space, E a topological vector space, V a Nachbin family of weights on X, and CV0(X,E) the weighted space of continuous E-valued functions on X. Let θ:X→C be a mapping, f∈CV0(X,E) and define Mθ(f)=θf (pointwise). In case E is a topological algebra, ψ:X→E is a mapping then define Mψ(f)=ψf (pointwise). The main purpose of this paper is to give necessary and sufficient conditions for Mθ and Mψ to be the multiplication operators on CV0(X,E) where E is a general topological space (or a suitable topological algebra) which is not necessarily locally convex. These results generalize recent work of Singh and Manhas based on the assumption that E is locally convex.http://dx.doi.org/10.1155/S0161171297000112Nachbin family of weightstopological vector spacesvector-valued continuous functionsweighted topologymultiplication operatorslocally idempotent topological algebras. |
| spellingShingle | L. A. Khan A. B. Thaheem Multiplication operators on weighted spaces in the non-locally convex framework International Journal of Mathematics and Mathematical Sciences Nachbin family of weights topological vector spaces vector-valued continuous functions weighted topology multiplication operators locally idempotent topological algebras. |
| title | Multiplication operators on weighted spaces in the non-locally convex framework |
| title_full | Multiplication operators on weighted spaces in the non-locally convex framework |
| title_fullStr | Multiplication operators on weighted spaces in the non-locally convex framework |
| title_full_unstemmed | Multiplication operators on weighted spaces in the non-locally convex framework |
| title_short | Multiplication operators on weighted spaces in the non-locally convex framework |
| title_sort | multiplication operators on weighted spaces in the non locally convex framework |
| topic | Nachbin family of weights topological vector spaces vector-valued continuous functions weighted topology multiplication operators locally idempotent topological algebras. |
| url | http://dx.doi.org/10.1155/S0161171297000112 |
| work_keys_str_mv | AT lakhan multiplicationoperatorsonweightedspacesinthenonlocallyconvexframework AT abthaheem multiplicationoperatorsonweightedspacesinthenonlocallyconvexframework |