Rocky Mountain Journal of Mathematics

A note on skew product preserving maps on factor von Neumann algebras

Ali Taghavi and Hamid Rohi

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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 $.

Article information

Source
Rocky Mountain J. Math., Volume 47, Number 6 (2017), 2083-2094.

Dates
First available in Project Euclid: 21 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1511254965

Digital Object Identifier
doi:10.1216/RMJ-2017-47-6-2083

Mathematical Reviews number (MathSciNet)
MR3725257

Zentralblatt MATH identifier
06816583

Subjects
Primary: 47B48: Operators on Banach algebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]

Keywords
Preserving problems skew products von Neumann algebras

Citation

Taghavi, Ali; Rohi, Hamid. A note on skew product preserving maps on factor von Neumann algebras. Rocky Mountain J. Math. 47 (2017), no. 6, 2083--2094. doi:10.1216/RMJ-2017-47-6-2083. https://projecteuclid.org/euclid.rmjm/1511254965


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