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Lie homomorphisms of
operator algebras
C. Robert Miers |
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Vol. 38 (1971), No. 3, 717–735
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Abstract |
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A mapping ϕ : M → N between ∗-algebras M,N which is ∗-linear, and which preserves the Lie bracket [X,Y ] = XY − Y X of elements X,Y in M is called a Lie ∗-homomorphism or just a Lie homomorphism. The main result of this paper states that if ϕ : A → B is a uniformly continuous Lie ∗-homomorphism of the C∗-algebra A onto the C∗-algebra B then there exists a central projection D in the weak closure of B such that modulo a center-valued ∗-linear map which annihilates brackets, Dϕ is a ∗-homomorphism and (I − D)ϕ is the negative of a ∗anti-homomorphism. |
Mathematical Subject Classification 2000
Primary: 46L10
Secondary: 46L05
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Milestones
Received: 30 December 1969
Revised: 30 April 1970
Published: 1 September 1971
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Authors |
| C. Robert Miers | |
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