Derivations with a Hereditary Domain | Zendy

Villena A. R. | Zendy

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Derivations with a Hereditary Domain

Author(s) -

Villena A. R.

Publication year - 1998

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610798006152

Subject(s) - subspace topology , subalgebra , property (philosophy) , domain (mathematical analysis) , pure mathematics , banach space , mathematics , banach algebra , algebra over a field , discrete mathematics , philosophy , mathematical analysis , epistemology

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[ B k ∩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 Y ( D ) for D satisfies the property B [ B ∩ Y ( 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.

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