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A SOBOLEV ALGEBRA OF VOLTERRA TYPE

Part of: Real functions Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  12 December 2012

JOSÉ E. GALÉ  and
LUIS SÁNCHEZ-LAJUSTICIA
JOSÉ E. GALÉ*
Affiliation:
Departamento de Matemáticas & IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain (email: gale@unizar.es)
LUIS SÁNCHEZ-LAJUSTICIA
Affiliation:
Departamento de Matemáticas & IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain (email: luiss@unizar.es)
*
✉For correspondence; e-mail: gale@unizar.es
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Abstract

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We present a family of radical convolution Banach algebras on intervals (0,a] which are of Sobolev type; that is, they are defined in terms of derivatives. Among other properties, it is shown that all epimorphisms and derivations of such algebras are bounded. Also, we give examples of nontrivial concrete derivations.

Keywords

radical Banach algebraconvolutionhigher-order absolutely continuous functionVolterra algebraderivation

MSC classification

Secondary: 46J45: Radical Banach algebras 26A46: Absolutely continuous functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 92 , Issue 3 , June 2012 , pp. 313 - 334
Copyright
Copyright © 2012 Australian Mathematical Publishing Association Inc.

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