【摘 要】
：
Let M;N be semi-finite von Neumann algebras with faithful semi-finite normal traces(τ) M,(τ) N,respectively.Suppose that φ : Lp(M,(τ) M)∩M+→Lp(N,(τ)
【机 构】
：
NationalSunYat-senUniversity,Kaohsiung,Taiwan
【出 处】
：
算子代数和调和分析2017年研讨会 (Workshop on Operator Algebras and Harmoni
论文部分内容阅读
Let M;N be semi-finite von Neumann algebras with faithful semi-finite normal traces(τ) M,(τ) N,respectively.Suppose that φ : Lp(M,(τ) M)∩M+→Lp(N,(τ) N)∩N+(1< p<+∞); is a surjective mapping satisfying that‖x+y‖p =‖φ(x)+φ(y)‖p for all x; y∈Lp(M,(τ) M)∩M+.Then there exist uniquely a Jordan *-isomorphism J of M onto N,and a positive selfadjoint operator h∈Lp(N,(τ) N)(h can be unbounded in N)affiliated with the center of N such that φ(x)= J(x)h,x∈Lp(M,(τ) M)∩M+(1)Suppose,in additional,that M or N is a factor,then φ is an isomorphism or an anti-isomorphism of M onto N,and h is proportional to the identity of N; so there exists uniquely a Jordan *-isomorphism J such that there exists uniquely a strictly positive number λ such that φ(x)= λJ(x)for every x∈Lp(M,(τ) M)∩M+.
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