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The Banach algebra induced by a double centralizer

Author: Etienne Desquith
Journal: Proc. Amer. Math. Soc. 131 (2003), 2109-2119
MSC (2000): Primary 47D30
Published electronically: February 11, 2003
MathSciNet review: 1963757
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Abstract: Given a Banach algebra $A$, R. Larsen defined, in his book ``An introduction to the theory of multipliers", a Banach algebra $A_{T}$ by means of a multiplier $T$ on $A$, and essentially used it in the case of a commutative semisimple Banach algebra $A$ to prove a result on multiplications which preserve regular maximal ideals. Here, we consider the analogue Banach algebra ${\mathcal A}_{R}$ induced by a bounded double centralizer $\langle L , R \rangle$ of a Banach algebra $A$. Then, our main concern is devoted to the relationships between $L$, $R$, and the algebras of bounded double centralizers ${\mathcal W}(A)$ and ${\mathcal W}({\mathcal A}_{R})$of $A$ and ${\mathcal A}_{R}$, respectively. By removing the assumption of semisimplicity, we generalize some results proven by Larsen.

References [Enhancements On Off] (What's this?)

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Additional Information

Etienne Desquith
Affiliation: Institut de Recherches Mathématiques (IRMA), 08 BP 2030 Abidjan 08, Ivory Coast

Keywords: Annihilator, Banach algebra, double centralizer, multiplier
Received by editor(s): November 28, 2001
Received by editor(s) in revised form: February 4, 2002
Published electronically: February 11, 2003
Additional Notes: This work was supported by the Abdus Salam ICTP Associateship scheme (Trieste/Italy)
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society