Rearrangements of Tripotents and Differences of Isometries in Semifinite von Neumann Algebras

被引：0

作者：

A. M. Bikchentaev

机构：

[1] Kazan (Volga region) Federal University,N. I. Lobachevskii Institute of Mathematics and Mechanics

来源：

Lobachevskii Journal of Mathematics | 2019年 / 40卷

关键词：

Hilbert space; linear operator; isometry; unitary operator; idempotent; tripotent; projection; compact operator; von Neumann algebra; trace; rearrangement;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let τ be a faithful normal semifinite trace on a von Neumann algebra ℳ, and ℳu be a unitary part of ℳ. We prove a new property of rearrangements of some tripotents in ℳ. If V ∈ ℳ is an isometry (or a coisometry) and U − V is τ-compact for some U ∈ ℳu then V ∈ ℳu. Let ℳ be a factor with a faithful normal trace τ on it. If V ∈ ℳ is an isometry (or a coisometry) and U − V is compact relative to ℳ for some U ∈ ℳu then V ∈ ℳu. We also obtain some corollaries.

引用

页码：1450 / 1454

页数：4

共 30 条

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