﻿ 半有限von Neumann代数上的逼近2-局部导子
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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (9): 1350-1354.  DOI: 10.11908/j.issn.0253-374x.2019.09.016 0

### 引用本文

ZHAO Xingpeng, FANG Xiaochun, YANG Bing. Approximately 2-Local Derivations on the Semi-finite von Neumann Algebras[J]. Journal of Tongji University (Natural Science), 2019, 47(9): 1350-1354. DOI: 10.11908/j.issn.0253-374x.2019.09.016

### 文章历史

1 预备知识

(1) 映射τ:$\mathscr{M}$+→[0, ∞]称为$\mathscr{M}$上的迹, 如果τ满足: ①对于$\mathscr{M}$+任意的2个元素xy以及任意的λ>0, 有τ(x+λy)=τ(x) +λτ(y); ②对于$\mathscr{M}$中的任意元素x, 有τ(x*x)=(xx*).

(2) 迹τ称为正规的, 如果对$\mathscr{M}$+中任一有界单增网{xi}有supiτ(xi)=τ(supixi); 称τ为有限的, 如果τ(1) < ∞; 称τ为半有限的, 如果对$\mathscr{M}$+的任一非零元x, 存在$\mathscr{M}$+中的一个非零元y, 使得yxτ(y) < ∞; 称τ为忠实的, 如果$\mathscr{M}$+中的元x使得τ(x)=0有x=0.

(3) 如果τ$\mathscr{M}$上的一个正规忠实的半有限迹, 称($\mathscr{M}$, τ)是一个非交换测度空间.

2 主要结果及其证明

3 结语

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