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Derivations mapping into the socle

Published online by Cambridge University Press:  24 October 2008

Matej Brešar  and
Peter Šemrl
Matej Brešar
Affiliation:
PF, University of Maribor, Koroška 160, 62000 Maribor, Slovenia
Peter Šemrl
Affiliation:
TF, University of Maribor, Smetanova 17, 62000 Maribor, Slovenia
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Extract

Over the last few years a number of results giving conditions on a derivation of a Banach algebra implying that its range is contained in the radical have been obtained (see survey articles of Mathieu[7] and Murphy [8]). If an algebra is semi-simple, these conditions, of course, imply that a derivation is zero. In this paper we consider inner derivations that are non-zero in general, but their ranges are rather special and ‘small’ in some sense.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 120 , Issue 2 , August 1996 , pp. 339 - 346
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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