Conjugation-invariant subspaces and Lie ideals in non-selfadjoint operator algebras

被引：13

作者：

Marcoux, LW ^{[1
]}

Sourour, AR

机构：

[1] Univ Alberta, Dept Math, Edmonton, AB T6G 2G1, Canada

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3P4, Canada

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2002年 / 65卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

D O I：

10.1112/S002461070100299X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that a weakly closed subspace G of a nest algebra A is closed under conjugation by invertible elements in A that is, a(-1) G a = G if and only if G is a Lie ideal. A similar result holds for not-necessarily-closed subspaces of algebras of infinite multiplicity. An explicit characterisation of weakly closed Lie ideals in a nest algebra is given.

引用

页码：493 / 512

页数：20

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