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November 2004 Calcul fonctionnel holomorphe dans les algèbres p-Banach quotients
Bouchra Aharmim, Hamid Arroub
Bull. Belg. Math. Soc. Simon Stevin 11(4): 625-633 (November 2004). DOI: 10.36045/bbms/1102689126

Abstract

Let $A$ be a p-Banach algebra and $\alpha$ a two-sided ideal of $A$ with a complete p-norm stronger than the p-norm inherited from $A$. By integral methods, we give here a holomorphic functional calculus relatively to $\alpha$ which coïncides with the holomorphic functional calculus defined in $A\vert\alpha$\, considered as a quotient quasi-Banach algebra. As application, we get a version of Šilov's decomposition theorem. We also give the spectral mapping theorem and an integral formula for the image of the k-th derivative of a holomorphic function.

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Bouchra Aharmim. Hamid Arroub. "Calcul fonctionnel holomorphe dans les algèbres p-Banach quotients." Bull. Belg. Math. Soc. Simon Stevin 11 (4) 625 - 633, November 2004. https://doi.org/10.36045/bbms/1102689126

Information

Published: November 2004
First available in Project Euclid: 10 December 2004

zbMATH: 1089.46028
MathSciNet: MR2115730
Digital Object Identifier: 10.36045/bbms/1102689126

Rights: Copyright © 2004 The Belgian Mathematical Society

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Vol.11 • No. 4 • November 2004
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