全正映射及其张量积  

Completely Positive Maps and Their Tensor Product

作　　者：陈青[1] 朱作桐[1] 

机构地区：[1]南京师范大学

出　　处：《哈尔滨师范大学自然科学学报》1990年第3期11-15,共5页Natural Science Journal of Harbin Normal University

摘　　要：本文讨论了C代数中的全正映射,推广了[1]中命题2.5的结果。本文利用[2]中的记号、设H_i是Hilbert空间,H_1(?)H_2是H_1与H_2的代数张量积,任给ξ=sum from I=1 to n ξ_(1I)(?)ξ_(2I)∈H_1(?)H_2,η=sum from j=1 to m η_(1j)(?)η_(2j)∈H_1(?)H_2,定义(ξ,η)=sum from n=I,j (ξ_(1i),η_(1j))(ξ_(2j),η_(2j)),由[2],(,)是H_1(?)H_2中的内积。H_1(?)H_2的完备化,用H_1(?)H_2表示,其是a是由H_1(?)H_2中内积导出的范数(见[1]p182)。In this paper, we discuss completely positive maps of C~*-algebras and generalize lemma 2.5 in[1] and proposition 4.23 in [2].We have shown following main results:Proposition 2:If ψ_i(i=1, 2)are completely positive maps of A_i into anoth er C~*-algebra B_i, then ψ_1(?)ψ_2: A_1(?)A_2→B_1(?)B_2 can be extended to a completely positive map of A_1(?)_(β0)A_2 into B_1(?)minB_2, where β_0 is any C~*-norm, ‖ ‖ min is the injective C~*-cross-norm.Corollary: If ψ_i:A_i→B_i is a completely positive map, A_i anb B_i are C~*-algebras, then ψ_1~*(?)ψ_2~*:B_1~*(?)_(β0)B_2*→A_1~*(?)min A_2~* is a completely positive map.

关 键 词：C^＊代数 全正映射 希氏空间 张量积 

分 类 号：O177.5[理学—数学]