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Theoretical analysis characterizes skew-product-preserving bijective maps on von Neumann algebras, establishing conditions for linear or conjugate linear star-isomorphisms.
Let [Formula: see text] and [Formula: see text] be von Neumann algebras. For [Formula: see text], define [Formula: see text], the product ⋆ of [Formula: see text] and [Formula: see text]. This manuscript discusses the bijective mapping [Formula: see text] that preserve the product ⋆ on von Neumann algebras [Formula: see text], for every [Formula: see text]. Especially, we elaborate on the characteristics of the map [Formula: see text]. Precisely, we establish the necessary and sufficient condition that [Formula: see text] is a linear ⋆-ring isomorphism or the negative of a conjugate linear ⋆-isomorphism
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Raza et al. (2026) studied this question.
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