June 2023 NONLINEAR MAPS PRESERVING THE MIXED PRODUCT ABC ON VON NEUMANN ALGEBRAS
Leila Abedini, Ali Taghavi
Rocky Mountain J. Math. 53(3): 671-678 (June 2023). DOI: 10.1216/rmj.2023.53.671

Abstract

Let 𝒜 and be two von Neumann algebras. For A,B𝒜, define AB=AB+BA and AB=ABBA to be the new products of A and B. Suppose that a bijective map Φ:𝒜 satisfies Φ(ABC)=Φ(A)Φ(B)Φ(C) for all A,B,C𝒜. In this paper, it is proved that if 𝒜 and are two von Neumann algebras with no central abelian projections, then the map Φ(I)Φ is the sum of a -isomorphism and a conjugate linear -isomorphism, where Φ(I) is a self-adjoint central element in with Φ(I)2=I.

Citation

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Leila Abedini. Ali Taghavi. "NONLINEAR MAPS PRESERVING THE MIXED PRODUCT ABC ON VON NEUMANN ALGEBRAS." Rocky Mountain J. Math. 53 (3) 671 - 678, June 2023. https://doi.org/10.1216/rmj.2023.53.671

Information

Received: 30 October 2021; Revised: 16 July 2022; Accepted: 10 August 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617903
zbMATH: 07731137
Digital Object Identifier: 10.1216/rmj.2023.53.671

Subjects:
Primary: 46J10 , 47B48

Keywords: isomorphism , Jordan ∗-product , von Neumann algebras

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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