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Similarité entre l'algèbre de Volterra et un quotient d'algèbre uniforme

Published online by Cambridge University Press:  20 January 2009

Konin Koua
Konin Koua
Affiliation:
Mathématiques et InformatiqueUniversité Bordeaux 1351 Cours de la Libération33405 Talence CedexFrance
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Abstract

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Two commutative Banach algebras A and B are said to be similar if there exists a Banach algebra D such that [xD]− = D for some x in D, and two one-to-one continuous homomorphisms φ:D→A and ψ:D→B such that φ(D) is a dense ideal of A and ψ(D) a dense ideal of B.

We prove in this paper that the Volterra algebra is similar to A0/e-z A0 where A0 is the commutative uniform, separable Banach algebra of all continuous functions on the closed right-hand half plane , analytic on H and vanishing at infinity. We deduce from this result that multiplication by an element of A0/e-z A0 is a compact mapping.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 3 , October 1991 , pp. 383 - 391
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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