J4 ›› 2010, Vol. 45 ›› Issue (2): 58-60.

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Lie-* derivations on factor von Neumann algebras

  

  • Received:2009-04-28 Online:2010-02-16 Published:2010-03-27

Abstract:

Let M be a factor von Neumann algebra acting on a complex separable Hilbert space H with dim H>2. If [WTBX]:〖WTHT〗M→M be a Lie* derivation, then (A)=AT-TA+h(A) for all A∈M, where T∈M, h:M→CI is a linear mapping with h(AB*-B*A)=0 for all A,B∈M and T+T*=βI, β∈R.

Key words: Lie-* derivation; von Neumann algebra; commuting trace

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