Characterization of normal traces on von Neumann algebras by inequalities for the modulus

被引：13

作者：

Stolyarov, AI ^{[1
]}

Tikhonov, OE ^{[1
]}

Sherstnev, AN ^{[1
]}

机构：

[1] Kazan VI Lenin State Univ, Kazan 420008, Russia

来源：

MATHEMATICAL NOTES | 2002年 / 72卷 / 3-4期

基金：

俄罗斯基础研究基金会;

关键词：

von Neumann algebra; normal semifinite weight; trace; ultrastrong topology; ultraweak topology;

D O I：

10.1023/A:1020559623287

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is proved that if a normal semifinite weight phi on a von Neumann algebra M satisfies the inequality phi(\a(1) + a(2)\) less than or equal to phi(\a(1)\) + phi(\a(2)\) for any selfadjoint operators a(1), a(2) in M, then this weight is a trace. Several similar characterizations of traces among the normal semifinite weights are proved. In particular, Gardner's result on the characterization of traces by the inequality \phi(a)\ less than or equal to phi(\a\) is refined and reinforced.

引用

页码：411 / 416

页数：6

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