A Characterization of Nonadditive Skew Commuting Maps on ∗-Algebras

Liang Kong and Chao Li

Journal of Mathematics, 2025, vol. 2025, 1-6

Abstract: Let A be a unital ∗-algebra with the unit I and ZSA be the symmetric center of A. Assume that A contains a nontrivial projection P such that AAP=0 implies A=0 and AAI−P=0 implies A=0. In this paper, we proved that if a map φ:A⟶A satisfies φA,B∗=−φB,A∗ for all A,B∈A, then there exists a map f:A⟶ZSA such that φA=ZA+fA for all A∈A, where ZA∈ZSA. As applications, we obtain the concrete form of nonadditive skew commuting maps on prime ∗-algebra, factor von Neumann algebras and standard operator algebras.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:6639975

DOI: 10.1155/jom/6639975

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