On invariant subspaces of operators in the class θ

[摘要] In this paper, we consider invariant subspaces of operators in the class theta, which is the set of operators T such that T*T and T + T* commute. It is shown that every operator in the class theta such that the outer boundary of its spectrum is the outer boundary of a Caratheodory domain has a nontrivial invariant subspace. We also give a family of operators in the class theta which are reductive, i.e., their invariant subspaces are reducing. In addition, we give a condition on spectra of operators in the class theta which gives some information about invariant subspaces. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Operator class theta;Invariant subspaces;Caratheodory domains;k-spectral sets