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  • Proceedings of the Edinburgh Mathematical Society, Volume 41, Issue 3
  • October 1998, pp. 625-630

Continuity of Lie derivations on Banach algebras

  • M. I. Berenguer (a1) and A. R. Villena (a1)
  • DOI:
  • Published online: 01 January 2009

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

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1.M. Brešar , Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings, Trans. Amer. Math. Soc. 335 (1993), 525546.

2.P. de la Harpe , Classical Banach-Lie algebras and Banach Lie groups of operators in Hilbert space (Lecture Notes in Math. 285, Springer-Verlag, Berlin, 1972).

3.I. N. Herstein , Lie and Jordan structures in simple, associative rings, Bull. Amer. Math. Soc. 67 (1961), 517531.

4.B. E. Johnson and A. M. Sinclair , Continuity of derivations and a problem of Kaplansky, Amer. J. Math. 90 (1968), 10671073.

6.W. S. Martindale , 3rd, Lie isomorphisms of prime rings, Trans. Amer. Math. Soc. 142 (1969), 437455.

7.C. R. Miers , Lie derivations of von Neumann algebras, Duke Math. J. 40 (1973), 403409.

8.C. R. Miers , Lie triple derivations of von Neumann algebras, Proc. Amer. Math. Soc. 71 (1978), 5761.

10.M. P. Thomas , Primitive derivations on non-commutative Banach algebras, Pacific J. Math. 159(1993), 139152.

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