Spectral Radius Algebras of Idempotents

被引：1
|
作者：
Herron, John David [1 ]
机构：
[1] Univ Montevallo, Dept Biol Chem & Math, Montevallo, AL 35115 USA
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2009年 / 64卷 / 02期
关键词：
Spectral radius algebra; idempotent; invariant subspace; INVARIANT SUBSPACES; OPERATORS; COMMUTATORS;
D O I：
10.1007/s00020-009-1684-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the spectral radius algebras of certain quadratic operators possess nontrivial invariant subspaces. Additionally, such algebras properly contain the operator's commutant, so that the invariant subspaces are in some sense beyond hyperinvariant. The spectral radius algebras of idempotents are completely described and, as a consequence, it is shown that every intransitive collection of operators must be contained in a norm-closed proper spectral radius algebra.
引用
收藏
页码：193 / 201
页数：9
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