Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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
  • 3. Ronald Larsen, An introduction to the theory of multipliers, Springer-Verlag, New York-Heidelberg, 1971. Die Grundlehren der mathematischen Wissenschaften, Band 175. MR 0435738
  • 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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47D30

Retrieve articles in all journals with MSC (2000): 47D30

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