Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-26T12:06:02.984Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)