完全保混合Lie零积的映射
Maps Completely Preserving Mixed Lie Zero Product
摘要: 本文刻画*代数上完全保混合Lie零积的非线性映射,利用该结论得到不含交换中心投影的von Neumann代数上*-同构的等价刻画。
Abstract: In this paper, we characterize nonlinear maps on *-algebras completely preserving mixed Lie zero products. As its application, equivalent characterization of *-isomorphism on von Neumann algebra with no abelian center projections is obtained.
文章引用:毛欢, 安润玲, 丁杰. 完全保混合Lie零积的映射[J]. 应用数学进展, 2025, 14(4): 579-583. https://doi.org/10.12677/aam.2025.144188

参考文献

[1] 白朝芳, 侯晋川. 保零积或约当零积的映射[J]. 数学年刊A辑, 2008, 29(5): 663-670.
[2] 齐霄霏, 侯晋川, 崔建莲. 保持斜ξ-Lie零积的可加映射[J]. 中国科学(数学), 2015, 45(2): 151-166.
[3] Wong, W. (1981) Maps on Simple Algebras Preserving Zero Products. II. Lie Algebras of Linear Type. Pacific Journal of Mathematics, 92, 469-488. [Google Scholar] [CrossRef
[4] Słowik, R. (2017) Maps on Upper Triangular Matrices Preserving Zero Products. Czechoslovak Mathematical Journal, 67, 1095-1103. [Google Scholar] [CrossRef
[5] Chen, L. and Wang, D. (2015) Nonlinear Bijective Maps on Strictly Upper Triangular Matrices Preserving Zero Product. Linear and Multilinear Algebra, 64, 412-425. [Google Scholar] [CrossRef
[6] Huang, L. and Liu, Y. (2014) Maps Completely Preserving Commutativity and Maps Completely Preserving Jordan Zero-Product. Linear Algebra and Its Applications, 462, 233-249. [Google Scholar] [CrossRef
[7] 付飞艳. von Neumann代数上导子与同构的等价刻画[D]: [硕士学位论文]. 太原: 太原理工大学, 2018.