因子von Neumann代数正锥上的凸序列积自同构  

Convex Sequential Product Automorphisms on the Positive Cone of a Factor von Neumann Algebra

作　　者：卜浪梅 吉国兴[1] Lang Mei BU;Guo Xing JI(School of Mathematics and Statistics,Shaanxi Normal University,Xi'an 710119,P.R.China)

机构地区：[1]陕西师范大学数学与统计学院,西安710119

出　　处：《数学学报（中文版）》2024年第3期521-530,共10页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(12271323)。

摘　　要：设H是复Hilbert空间,M是H上维数大于1的因子von Neumann代数,M+是M的正锥.设λ∈[0,1],定义Ao_λ=λA1/2BA1/2+(1-λ)B1/2AB1/2,?A,B∈M+,称o_λ为M+上的凸序列积.本文证明了M+上的凸序列积自同构是由M的一个*-同构或*-反同构实现.Let M be a factor von Neumann algebra on a complex Hilbert space H with dim M>1 and M_+the positive cone of M.We consider automorphisms of M_+with respect to convex sequential product o_λon M_+for someλ∈[0,1]defined by A o_λB=λA~(1/2)BA~(1/2)+(1-λ)B~(1/2)AB~(1/2)for any A,B∈M_+.We show that an automorphism of M_+with respect to convex sequential product is implemented by a*-isomorphism or an anti-*-isomorphism of M.

关 键 词：因子von Neumann代数 正锥 凸序列积 自同构 

分 类 号：O177.1[理学—数学]