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DERIVATIONS WITH A HEREDITARY DOMAIN

Published online by Cambridge University Press:  01 April 1998

A. R. VILLENA
A. R. VILLENA
Affiliation:
Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain. E-mail: avillena@goliat.ugr.es
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Abstract

We investigate the closability of those derivations D defined on a (non necessarily closed) subalgebra B of a complex Banach algebra A for which the conditions

BAB⊂B and dim[Bk∩Rad(A)]<∞

hold for some k∈ℕ, where Rad(A) stands for the Jacobson radical of A. In this situation we show that the separating subspace [Sscr ](D) for D satisfies the property

B[B∩[Sscr ](D)]B⊂Rad(A).

Furthermore, we demonstrate several specially relevant situations in which we get a ‘closability property’ which is more precise than the former one.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 2 , April 1998 , pp. 469 - 477
Copyright
The London Mathematical Society 1998

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