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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

REFERENCES

[1]Alexander, J. C.. Compact Banach Algebras. Proc. London Math. Soc. 18 (1968), 1–18.CrossRefGoogle Scholar
[2]Aupetit, B.. A primer on spectral theory (Springer-Verlag, 1991).CrossRefGoogle Scholar
[3]Bonsall, F. F. and Duncan, J.. Complete normed algebras (Springer, 1973).CrossRefGoogle Scholar
[4]Fell, J. M. G. and Doran, R. S.. Repnsentations of *-algebras, locally compact groups, and Banach *-algebraic bundles, vol. 1 (Academic Press, 1988).Google Scholar
[5]Lanski, C.. Derivations with algebraic values on Lie ideals. Comm. Algebra 18 (1990), 1379–1399.CrossRefGoogle Scholar
[6]Lindenstrauss, J. and Tzafriri, L.. Classical Banach spaces, Part I: sequence spaces (Springer, 1977).CrossRefGoogle Scholar
[7]Mathieu, M.. Where to find the image of a derivation, in Functional analysis and operator theory, Banach Center Publications, vol. 30 (Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1994), 237–249.Google Scholar
[8]Murphy, G. J.. Aspects of the theory of derivations, in Functional analysis and operator theory, Banach Center Publications, vol. 30 (Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1994), 267–275.Google Scholar
[9]Rickart, C. E.. General theory of Banach algebras (van Nostrand, 1960).Google Scholar