Banach Journal of Mathematical Analysis

Quasi-multipliers of the dual of a Banach algebra

M. Adib, J. Bracic, and A. Riazi

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In this paper we extend the notion of quasi-multipliers to the dual of a Banach algebra $A$ whose second dual has a mixed identity. We consider algebras satisfying weaker condition than Arens regularity. Among others we prove that for an Arens regular Banach algebra which has a bounded approximate identity the space $QM_{r}(A^{*})$ of all bilinear and separately continuous right quasi-multipliers of $A^{*}$ is isometrically isomorphic to $A^{**}.$ We discuss the strict topology on $QM_{r}(A^{*})$ and apply our results to $C^{*}-$algebras and to the group algebra of a compact group.

Article information

Banach J. Math. Anal., Volume 5, Number 2 (2011), 6-14.

First available in Project Euclid: 14 August 2011

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Zentralblatt MATH identifier

Primary: 47B48: Operators on Banach algebras
Secondary: 46H25: Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX)

quasi-multiplier multiplier Banach algebra second dual Arens regularity


Adib, M.; Riazi, A.; Bracic, J. Quasi-multipliers of the dual of a Banach algebra. Banach J. Math. Anal. 5 (2011), no. 2, 6--14. doi:10.15352/bjma/1313362997.

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