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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.