Multipliers of Modules of Continuous Vector-Valued Functions
In 1961, Wang showed that if A is the commutative C*-algebra C0(X) with X a locally compact Hausdorff space, then M(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/397376 |
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| author | Liaqat Ali Khan Saud M. Alsulami |
| author_facet | Liaqat Ali Khan Saud M. Alsulami |
| author_sort | Liaqat Ali Khan |
| collection | DOAJ |
| description | In 1961, Wang showed that if A is the commutative C*-algebra C0(X) with X a locally compact Hausdorff space, then M(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing that HomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)), where E and F are p-normed spaces which are also essential isometric left A-modules with A being a certain commutative F-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature. |
| format | Article |
| id | doaj-art-945607434cfe4b90bfe4e4b970b40aef |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-945607434cfe4b90bfe4e4b970b40aef2025-02-03T01:27:51ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/397376397376Multipliers of Modules of Continuous Vector-Valued FunctionsLiaqat Ali Khan0Saud M. Alsulami1Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaIn 1961, Wang showed that if A is the commutative C*-algebra C0(X) with X a locally compact Hausdorff space, then M(C0(X))≅Cb(X). Later, this type of characterization of multipliers of spaces of continuous scalar-valued functions has also been generalized to algebras and modules of continuous vector-valued functions by several authors. In this paper, we obtain further extension of these results by showing that HomC0(X,A)(C0(X,E),C0(X,F))≃Cs,b(X,HomA(E,F)), where E and F are p-normed spaces which are also essential isometric left A-modules with A being a certain commutative F-algebra, not necessarily locally convex. Our results unify and extend several known results in the literature.http://dx.doi.org/10.1155/2014/397376 |
| spellingShingle | Liaqat Ali Khan Saud M. Alsulami Multipliers of Modules of Continuous Vector-Valued Functions Abstract and Applied Analysis |
| title | Multipliers of Modules of Continuous Vector-Valued Functions |
| title_full | Multipliers of Modules of Continuous Vector-Valued Functions |
| title_fullStr | Multipliers of Modules of Continuous Vector-Valued Functions |
| title_full_unstemmed | Multipliers of Modules of Continuous Vector-Valued Functions |
| title_short | Multipliers of Modules of Continuous Vector-Valued Functions |
| title_sort | multipliers of modules of continuous vector valued functions |
| url | http://dx.doi.org/10.1155/2014/397376 |
| work_keys_str_mv | AT liaqatalikhan multipliersofmodulesofcontinuousvectorvaluedfunctions AT saudmalsulami multipliersofmodulesofcontinuousvectorvaluedfunctions |