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Additive Hermitian idempotent preservers between operator algebras
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-24 , DOI: 10.1016/j.jmaa.2021.125522 Chi-Kwong Li , Ming-Cheng Tsai , Ya-Shu Wang , Ngai-Ching Wong
中文翻译:
算子代数之间的加法 Hermitian 幂等保护器
更新日期:2021-07-30
Journal of Mathematical Analysis and Applications ( IF 1.2 ) Pub Date : 2021-07-24 , DOI: 10.1016/j.jmaa.2021.125522 Chi-Kwong Li , Ming-Cheng Tsai , Ya-Shu Wang , Ngai-Ching Wong
Let L be an additive map between (real or complex) matrix algebras sending Hermitian idempotent matrices to Hermitian idempotent matrices. We show that there are nonnegative integers with and an unitary matrix U such that We also extend this result to the (complex) von Neumann algebra setting, and provide a supplement to the Dye-Bunce-Wright Theorem asserting that every additive map of Hermitian idempotents extends to a Jordan ⁎-homomorphism.
中文翻译:
算子代数之间的加法 Hermitian 幂等保护器
令L是(实数或复数)矩阵代数发送之间的加法映射 Hermitian 幂等矩阵 厄米幂等矩阵。我们证明存在非负整数 和 和 酉矩阵U使得 我们还将这个结果扩展到(复杂的)von Neumann 代数设置,并提供对 Dye-Bunce-Wright 定理的补充,该定理断言 Hermitian 幂等的每个加法映射都扩展到 Jordan ⁎-同态。