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Let \(\mathscr {R}\) and \(\mathscr {K}\) be \(*\) -algebras with unity such that \(\mathscr {R}\) possesses a nontrivial projection \(P_1\) . In the current paper, we illustrate, under specific conditions that if a bijective map \(\Psi :\mathscr {R}\rightarrow \mathscr {K}\) satisfies \(\Psi (M\diamond N \bullet W)=\Psi (M)\diamond \Psi (N)\bullet \Psi (W)\) , where \(M\diamond N=M^*N+N^*M\) and \(M\bullet N=MN+NM^*\) for all \(M, N, W \in \mathscr {R}\) , then \(\Psi \) is a \(*\) -preserving ring isomorphism. Furthermore, this result is investigated in different algebras.

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A Note on Nonlinear Maps Preserving the Skew-Jordan-Type Products on \(*\) -Algebras

  • 会议论文

  • 发表日期：

    2025年

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  • Mohammad Aslam Siddeeque,
  • Raof Ahmad Bhat,
  • Mohammad Shane Alam

摘要

Let \(\mathscr {R}\) and \(\mathscr {K}\) be \(*\) -algebras with unity such that \(\mathscr {R}\) possesses a nontrivial projection \(P_1\) . In the current paper, we illustrate, under specific conditions that if a bijective map \(\Psi :\mathscr {R}\rightarrow \mathscr {K}\) satisfies \(\Psi (M\diamond N \bullet W)=\Psi (M)\diamond \Psi (N)\bullet \Psi (W)\) , where \(M\diamond N=M^*N+N^*M\) and \(M\bullet N=MN+NM^*\) for all \(M, N, W \in \mathscr {R}\) , then \(\Psi \) is a \(*\) -preserving ring isomorphism. Furthermore, this result is investigated in different algebras.