On invariant subspaces of operators in the class

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• 作者：Jaewoong Kim
• 关键词：Operator class ¦È ; Invariant subspaces ; Carathé ; odory domains ; k-spectral sets
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2012
• 出版时间：15 December, 2012
• 年：2012
• 卷：396
• 期：2
• 页码：562-568
• 全文大小：224 K

文摘

In this paper, we consider invariant subspaces of operators in the class , which is the set of operators such that and commute. It is shown that every operator in the class such that the outer boundary of its spectrum is the outer boundary of a Carath¨¦odory domain has a nontrivial invariant subspace. We also give a family of operators in the class which are reductive, i.e., their invariant subspaces are reducing. In addition, we give a condition on spectra of operators in the class which gives some information about invariant subspaces.