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Maps preserving productsXY−YX⁎on von Neumann algebras by Zhaofang Bai; Shuanping Du is a Mathematics article available to read on EtoBox.

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Let M, N be von Neumann algebras with no central summands of type I 1 . For T , S ∈ M, define [T , S] \* = T S -S T \* a new product of T and S. In this note, it is proved that a not necessarily linear bijective map Φ : M → N satisfies Φ([T , S] \* ) = [Φ(T ), Φ(S)] \* for all T , S ∈ M if and only if Φ is the direct sum of a linear \* -isomorphism and a conjugate linear \* -isomorphism.

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Author

Zhaofang Bai; Shuanping Du

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0022-247X)

Published

2012

Language

EN

Field

Mathematics (Physical Sciences)