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2017 A note on skew product preserving maps on factor von Neumann algebras
Ali Taghavi, Hamid Rohi
Rocky Mountain J. Math. 47(6): 2083-2094 (2017). DOI: 10.1216/RMJ-2017-47-6-2083

Abstract

Let $\mathcal {A}$ be a factor von Neumann algebra, with unit $ I $, which contains a nontrivial projection $ P_{1} $, and let $\psi :\mathcal {A} \rightarrow \mathcal {A}$ be a surjective map that satisfies one of the two conditions: $\psi (A)\psi (P) + \lambda \psi (P)\psi (A) = AP + \lambda PA$ and $\psi (A)\psi (P) + \lambda \psi (P)\psi (A)^{\ast } = AP + \lambda PA^{\ast }$ for all $A \in \mathcal {A}$ and $P \in \lbrace P_{1}, I - P_{1}\rbrace $ and $\lambda \in \lbrace -1, 1\rbrace $. Then, we determine the concrete form of $\psi $.

Citation

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Ali Taghavi. Hamid Rohi. "A note on skew product preserving maps on factor von Neumann algebras." Rocky Mountain J. Math. 47 (6) 2083 - 2094, 2017. https://doi.org/10.1216/RMJ-2017-47-6-2083

Information

Published: 2017
First available in Project Euclid: 21 November 2017

zbMATH: 06816583
MathSciNet: MR3725257
Digital Object Identifier: 10.1216/RMJ-2017-47-6-2083

Subjects:
Primary: 46J10 , 47B48

Keywords: Preserving problems , skew products , von Neumann algebras

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 6 • 2017
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