Nonlinear maps preserving mixed Jordan triple η-*-products on von Neumann  

Von Neumann代数上保持混合Jordan三重η-*-积的非线性映射

作　　者：PANG Yongfeng HUANG Beilei ZHANG Danli 庞永锋;黄蓓蕾;张丹莉(西安建筑科技大学理学院,陕西西安710055)

机构地区：[1]School of Science,Xi'an University of Architecture and Technology,Xi′an 710055,China

出　　处：《纯粹数学与应用数学》2025年第1期114-137,共24页Pure and Applied Mathematics

基　　金：国家自然科学基金(12061031);陕西省自然科学基金(2023-JC-YB-627).

摘　　要：Let M and N be two factor von Neumann algebras that their dimensions are large than 1,η≠-1 a non zero complex number and Φa(not necessary linear)bijection between two factor von Neumann algebras satisfying Φ(I)=I.For all A,B∈M,define by A■B=AB+BA the Jordan product of A and B,A·_(η)B=AB+ηBA^(*)the Jordan η-*-product of A and B,respectively.Let Φ and Φ^(-1)preserve the mixed Jordan triple η-*-products.It is proved that Φ is a linear *-isomorphism if η is not real and Φ is the sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real.设M和N是2个维数大于1的因子von Neumann代数,η≠-1是一个非零复数,Φ:M→N是因子von Neumann代数上的一个非线性映射且Φ(I)=I.对于任意,A,B∈M,定义A(?)B=AB+BA是A和B的Jordan积,A·_(η)B=AB+ηBA^(*)是A和B的Jordan η-*-积.设Φ和Φ-1保持混合Jordan三重η-*-积,则当η∈CR时,Φ是一个线性*-同构;当η∈R{0}时,Φ是一个线性*-同构和一个共轭线性*-同构之和.

关 键 词：factor von Neumann algebras mixed Jordan tripleη-*-products ISOMORPHISM 

分 类 号：O177.1[理学—数学]