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Continuity of Lie derivations on Banach algebras

Published online by Cambridge University Press:  20 January 2009

M. I. Berenguer  and
A. R. Villena
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Abstract

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The separating subspace of any Lie derivation on a semisimple Banach algebra A is contained in the centre of A.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 41 , Issue 3 , October 1998 , pp. 625 - 630
Copyright
Copyright © Edinburgh Mathematical Society 1998

References

REFERENCES

1. Brešar, M., Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525–546.CrossRefGoogle Scholar
2. de la Harpe, P., Classical Banach-Lie algebras and Banach Lie groups of operators in Hilbert space (Lecture Notes in Math. 285, Springer-Verlag, Berlin, 1972).CrossRefGoogle Scholar
3. Herstein, I. N., Lie and Jordan structures in simple, associative rings, Bull. Amer. Math. Soc. 67 (1961), 517–531.CrossRefGoogle Scholar
4. Johnson, B. E. and Sinclair, A. M., Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 1067–1073.CrossRefGoogle Scholar
5. Martindale, W. S., 3rd, Lie derivations of primitive rings, Michigan Math. J. 11 (1964), 183–187.CrossRefGoogle Scholar
6. Martindale, W. S., 3rd, Lie isomorphisms of prime rings, Trans. Amer. Math. Soc. 142 (1969), 437–455.CrossRefGoogle Scholar
7. Miers, C. R., Lie derivations of von Neumann algebras, Duke Math. J. 40 (1973), 403–409.CrossRefGoogle Scholar
8. Miers, C. R., Lie triple derivations of von Neumann algebras, Proc. Amer. Math. Soc. 71 (1978), 57–61.CrossRefGoogle Scholar
9. Palmer, T. W., Banach Algebras and the General Theory of *-algebras. Volume I: Algebras and Banach Algebras (Cambridge University Press, 1994).CrossRefGoogle Scholar
10. Thomas, M. P., Primitive derivations on non-commutative Banach algebras, Pacific J. Math. 159(1993), 139–152.CrossRefGoogle Scholar