Orthogonality Property \(\mathcal {O}\) and Compact Perturbations

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• 作者：Chun Guang Li ; Ting Ting Zhou
• 关键词：Orthogonality property \(\mathcal {O}\) ; Compact perturbations ; Function of operators
• 刊名：Complex Analysis and Operator Theory
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：10
• 期：8
• 页码：1741-1755
• 全文大小：496 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Operator Theory
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1661-8262
• 卷排序：10

文摘

A bounded linear operator T acting on a Hilbert space is said to have orthogonality property \(\mathcal {O}\) if the subspaces \(\ker (T-\alpha )\) and \(\ker (T-\beta )\) are orthogonal for all \(\alpha , \beta \in \sigma _p(T)\) with \(\alpha \ne \beta \). In this paper, the authors investigate the compact perturbations of operators with orthogonality property \(\mathcal {O}\). We give a sufficient and necessary condition to determine when an operator T has the following property: for each \(\varepsilon >0\), there exists \(K\in \mathcal {K(H)}\) with \(\Vert K\Vert <\varepsilon \) such that \(T+K\) has orthogonality property \(\mathcal {O}\). Also, we study the stability of orthogonality property \(\mathcal {O}\) under small compact perturbations and analytic functional calculus.