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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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?)

  • 1. Desquith, E.: Banach algebras associated to bounded module maps; Preprint ICTP $N^{0}$ IC 98/194; (1998).
  • 2. J. M. G. Fell and R. S. Doran, Representations of *-algebras, locally compact groups, and Banach *-algebraic bundles. Vol. 2, Pure and Applied Mathematics, vol. 126, Academic Press Inc., Boston, MA, 1988. Banach *-algebraic bundles, induced representations, and the generalized Mackey analysis. MR 936629 (90c:46002)
  • 3. Ronald Larsen, An introduction to the theory of multipliers, Springer-Verlag, New York, 1971. Die Grundlehren der mathematischen Wissenschaften, Band 175. MR 0435738 (55 #8695)
  • 4. Theodore W. Palmer, Banach algebras and the general theory of *-algebras. Vol. I, Encyclopedia of Mathematics and its Applications, vol. 49, Cambridge University Press, Cambridge, 1994. Algebras and Banach algebras. MR 1270014 (95c:46002)

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Additional Information

Etienne Desquith
Affiliation: Institut de Recherches Mathématiques (IRMA), 08 BP 2030 Abidjan 08, Ivory Coast
Email: desquith@hotmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06807-2
PII: S 0002-9939(03)06807-2
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