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

Daoui, A.; Mahzouli, H.; Zerouali, E.

doi:10.1090/S0002-9939-03-06904-1

Sur les algèbres $S$-régulières et la $S$-décomposabilité des opérateurs de multiplication
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by A. Daoui, H. Mahzouli and E. H. Zerouali PDF

Proc. Amer. Math. Soc. 131 (2003), 3211-3220 Request permission

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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