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Derivations with a Hereditary Domain

Authors:	Villena A R

Institution:	Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada 18071 Granada, Spain. E-mail: avillena{at}goliat.ugr.es

Abstract:	We investigate the closability of those derivations D definedon a (non necessarily closed) subalgebra B of a complex Banachalgebra A for which the conditions BAB $sub$ B and dimB^k ${cap}$ Rad(A)]< ${infty}$ hold for some k $isin$ N, where Rad(A) stands for the Jacobson radicalof A. In this situation we show that the separating subspaceY(D) for D satisfies the property BB ${cap}$ Y(D)]B $sub$ Rad(A). Furthermore, we demonstrate several specially relevant situationsin which we get a ‘closability property’ which ismore precise than the former one.

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