Minimality of convergence in measure topologies on finite von Neumann algebras

被引：16

作者：

Bikchentaev, AM ^{[1
]}

机构：

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

来源：

MATHEMATICAL NOTES | 2004年 / 75卷 / 3-4期

关键词：

*-algebra of measurable operators; metric ideal space; von Neumann algebra; convergence in measure;

D O I：

10.1023/B:MATN.0000023310.15215.c6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that the natural embedding of the metric ideal space on a finite von Neumann algebra M into the (*)-algebra of measurable operators (M) over tilde endowed with the topology of convergence in measure is continuous. Using this fact, we prove that the topology of convergence in measure is a minimal one among all metrizable topologies consistent with the ring structure on (M) over tilde.

引用

页码：315 / 321

页数：7

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