On a property of Lp spaces on semifinite von Neumann algebras

被引：25

作者：

Bikchentaev, AM ^{[1
]}

机构：

[1] Kazan State Univ, Kazan 420008, Russia

来源：

MATHEMATICAL NOTES | 1998年 / 64卷 / 1-2期

关键词：

von Neumann algebra; affiliated operator; trace; weight; Jordan algebra; logic of orthoprojections; measure on projections; noncommutative integration; Kothe duality;

D O I：

10.1007/BF02310299

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A characterization of the traces in a broad class of weights on von Neumann algebras is obtained. A new property of the "domain ideals" of these traces is proved. In the semifinite case, a relation for a faithful normal trace is established. This result is new even for the algebra of all bounded operators on a Hilbert space. Applications of the main result to the structure theory of von Neumann algebras and to the Kothe duality theory for ideal spaces of Segal measurable operators are given.

引用

页码：159 / 163

页数：5

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