Year: 2026
Type: article
Abstract: This work focuses on characterizing structure-preserving maps between factor von Neumann algebras with respect to a class of mixed skew Lie–Jordan $$n$$ n -products. Specifically, we consider expressions of the form $$ [A_1, A_2]_*\circ A_3 \circ \cdots \circ A_n, $$ [ A 1 , A 2 ] ∗ ∘ A 3 ∘ ⋯ ∘ A n , where each $$A_i \in \mathfrak {S}$$ A i ∈ S and $$\mathfrak {S}$$ S is a factor von Neumann algebra. Here, the skew Lie product is defined by $$[A_1, A_2]_*= A_1A_2 - A_2^*A_1$$ [ A 1 , A 2 ] ∗ = A 1 A 2 - A 2 ∗ A 1 , and the Jordan product by $$A_1 \circ A_2 = A_1A_2 + A_2A_1$$ A 1 ∘ A 2 = A 1 A 2 + A 2 A 1 . We prove that any map preserving these mixed products is necessarily a linear $$*$$ ∗ -isomorphism.
Source: Ricerche di Matematica
Institutions: Universidade Federal do ABC, Aligarh Muslim University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7153982847