2003
DOI: 10.1090/s0002-9939-03-06904-1
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Sur les algèbres $S$-régulières et la $S$-décomposabilité des opérateurs de multiplication

Abstract: Abstract. Let A be a commutative Banach algebra and ∆(A) its maximal ideal space. For given S ⊂ ∆(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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Cited by 2 publications
(9 citation statements)
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“…We give the following easy example to demonstrate this. This example also shows that a union of open t-analytic sets need not be t-analytic, contrary to an implicit assumption made in [8] Let X be a (non-empty) compact set in C and X • its interior. Then A(X) denotes the uniform algebra {f ∈ C(X) : f is analytic on X • }.…”
Section: T-analyticitymentioning
confidence: 85%
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“…We give the following easy example to demonstrate this. This example also shows that a union of open t-analytic sets need not be t-analytic, contrary to an implicit assumption made in [8] Let X be a (non-empty) compact set in C and X • its interior. Then A(X) denotes the uniform algebra {f ∈ C(X) : f is analytic on X • }.…”
Section: T-analyticitymentioning
confidence: 85%
“…In this note we will show that some refinements of notions appearing in a paper by Daoui, Mahzouli and Zerouali [8] in connection with local/restricted decomposability of multiplication operators on commutative, semisimple Banach algebras have a close connection with Alling's conjecture on the structure of closed prime ideals in H ∞ .…”
Section: Introductionmentioning
confidence: 86%
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