ADDITIVITY OF LIE MAPS ON OPERATOR ALGEBRAS

Title & Authors
ADDITIVITY OF LIE MAPS ON OPERATOR ALGEBRAS
Qian, Jia; Li, Pengtong;

Abstract
Let A standard operator algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If $\small{{\Phi}}$ is a bijective Lie map from A onto an arbitrary algebra, that is $\small{{\phi}}$(AB-BA)=$\small{{\phi}(A){\phi}(B)-{\phi}(B){\phi}(A)}$ for all A, B$\small{{\in}}$A, then $\small{{\phi}}$ is additive. Also, if A contains the identity operator, then there exists a bijective Lie map of A which is not additive.
Keywords
Language
English
Cited by
1.
Maps preserving -Lie product on factor von Neumann algebras, Linear and Multilinear Algebra, 2016, 64, 11, 2159
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