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Document Type |
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Thesis |
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Document Title |
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Quasi-Multipliers on A*- algebras شبة المضاعفات على A*- الجبري |
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Subject |
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mathematics department |
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Document Language |
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Arabic |
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Abstract |
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A quasi-multiplier m on an algebra A as a bilinear mapping from A x A into itself such that
m(ax,yb) = am(x,y)b for all a,x,y, b in A.
It is a generalization of the notion of a left (right, double) multiplier, and was first introduced by Akemann and Pedersen in 1973. The first system¬atic account of the general theory of quasi-multipliers on a Banach algebra with a bounded approximate identity was given in a paper by McKennon in 1977. Further developments have been made in recent years by many authors. The study of quasi-multipliers is presently an interesting area of research. In this thesis, we give an update study of the theory of quasi-multipliers on Banach algebras with minimal approximate identities In the initial three chapters, we include the fundamental definitions and results on Topology and Functional Analysis as well as both the algebraic and topological prop¬erties of various classes of multipliers on Banach algebras and A *-algebras. In the last two chapters, we consider the uniform, strict and quasi-strict topologies on the algebra QM{A) of all continuous bilinear quasi-multipliers on Banach algebras A having minimal ultra-approximate identities. We also consider extension properties of quasi-multipliers from a Banach al¬gebra A to its second dual space A**, when it is considered as an algebra under the Arens product. These include the embedding of QM(A) into A**. In particular, we give a unified and updated progress of research in this field. |
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Supervisor |
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Dr. Liaqat Ali Khan |
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Thesis Type |
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Master Thesis |
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Publishing Year |
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1433 AH
2012 AD |
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Added Date |
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Tuesday, June 5, 2012 |
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Researchers
| سلطان عثمان الغامدي | Al-Ghamdi, Sultan Othman | Researcher | Master | |
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