Bulletin of the Iranian Mathematical Society

Bulletin of the Iranian Mathematical Society

Some topologies on the space of quasi-multipliers

Document Type : Research Paper

Author
M. Adib
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 $A^{***}.$
Keywords
Quasi-multiplier‎
‎multiplier‎
‎Banach algebra‎
‎Arens regularity‎
‎strict topology‎
Subjects
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Bulletin of the Iranian Mathematical Society
Volume 43, Issue 5
October 2017
Pages 1323-1332

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