Maps Preserving n-tuple Product A * B + BA * on von Neumann Algebras

CRC Press eBooks 2026 Book chapter

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Authors: Alireza Ahalili Asboei, Mohammad Ahavandi, Amin Akbarzadeh
DOI: 10.1201/9781003647355-7
Cited by: 0

Abstract

Let A and B be two von Neumann algebras, and let Φ : A →B be a bijective map satisfying https://www.w3.org/1998/Math/MathML" display="block"> Φ ( A 1 ⋅ A 2 ⋅ … ⋅ An ) = Φ ( A 1 ) ⋅ Φ ( A 2 ) ⋅ … ⋅ Φ ( An ) , where Ai •Aj =A*i Aj+AjA*i for all Ai,Aj ∈A and i, j ∈ {1,2, ..., n}. Then, Φ is additive. Furthermore, if Φ(I) is self-adjoint, then Φ is an R-linear *-isomorphism.

Fields of Study & Subjects

Advanced Operator Algebra Research Advanced Topics in Algebra Rings Modules and Algebras

Publication details

Journal / source
CRC Press eBooks
Pages
115–129
Publication date
23 February 2026
Language
EN
Document type
Book chapter