# Some topologies on the space of quasi-multipliers

Document Type: Research Paper

Author

Department of Mathematics‎, ‎Payamenoor university(PNU)‎, ‎Tehran‎, ‎Iran.

Abstract

‎Assume that $A$ is a Banach algebra‎. ‎We define the‎ ‎$\beta-$topology and the $\gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$‎ ‎We establish further properties of $(QM_{el}(A^{*}),\gamma)$ when $A$ is a $C^{*}-$algebra‎. ‎In particular‎, ‎we characterize the $\gamma-$dual‎ ‎of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),\gamma)^{*},$ under the topology of bounded convergence‎, ‎is isomorphic to $A^{***}.$

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### History

• Receive Date: 26 February 2016
• Revise Date: 20 May 2016
• Accept Date: 31 May 2016