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Title

Derivations with a hereditary domain, II

Authors 1

Affiliations

  1. Departamento de Analisis Matematico, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain

Abstract

The nilpotency of the separating subspace of an everywhere defined derivation on a Banach algebra is an intriguing question which remains still unsolved, even for commutative Banach algebras. On the other hand, closability of partially defined derivations on Banach algebras is a fundamental problem motivated by the study of time evolution of quantum systems. We show that the separating subspace S(D) of a Jordan derivation defined on a subalgebra B of a complex Banach algebra A satisfies B[B∩S(D)]B⊂RadB(A) provided that BAB ⊂ A and dim(RadJ(A)∩⋂n=1∞Bn)<∞, where RadJ(A) and RadB(A) denote the Jacobson and the Baer radicals of A respectively. From this we deduce the closability of partially defined derivations on complex semiprime Banach algebras with appropriate domains. The result applies to several relevant classes of algebras.

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Studia Mathematica
1998/130/3
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Pages:
275-291
Main language of publication
English
Received
1997-10-10
Accepted
1997-12-22
Published
1998
Exact and natural sciences