rthogonality Property $$\mathcal {}$$ and Compact Perturbations |
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Authors: | Chun Guang Li Ting Ting Zhou |
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Institution: | 1.Department of Mathematics,Hebei Normal University,Shijiazhuang,China;2.School of Mathematics and Statistics,Northeast Normal University,Changchun,China;3.Department of Mathematics,Jilin University,Changchun,China |
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Abstract: | 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. |
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