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

 

Sur les algèbres $S$-régulières et la $S$-décomposabilité des opérateurs de multiplication


Authors: A. Daoui, H. Mahzouli and E. H. Zerouali
Journal: Proc. Amer. Math. Soc. 131 (2003), 3211-3220
MSC (2000): Primary 47B40, 47B48; Secondary 47A11
Published electronically: February 6, 2003
MathSciNet review: 1992862
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Abstract: Let $A$ be a commutative Banach algebra and $\Delta (A)$ its maximal ideal space. For given $S \subset \Delta (A)$, we establish necessary and sufficient conditions so that $A$ becomes $S$-regular. We derive some characterizations of decomposable multiplication operators and a description of the Apostol algebra of $A$. This provides a class of algebras(including Douglas algebras) for which the Apostol algebra is regular.


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Additional Information

A. Daoui
Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
Email: daoui@fsr.ac.ma

H. Mahzouli
Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
Email: houssame.mahzouli@caramail.com

E. H. Zerouali
Affiliation: Faculté des Sciences de Rabat, Département de Mathematiques et Informatique, BP 1014 Agdal, Rabat, Morocco
Email: zerouali@fsr.ac.ma

DOI: http://dx.doi.org/10.1090/S0002-9939-03-06904-1
PII: S 0002-9939(03)06904-1
Received by editor(s): June 29, 2000
Received by editor(s) in revised form: May 19, 2002
Published electronically: February 6, 2003
Communicated by: David R. Larson
Article copyright: © Copyright 2003 American Mathematical Society