SVEP and compact perturbations |
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Authors: | Sen Zhu Chun Guang Li |
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Institution: | a Department of Mathematics, Jilin University, Changchun 130012, PR China b Institute of Mathematics, Jilin University, Changchun 130012, PR China |
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Abstract: | Let H be a complex separable infinite dimensional Hilbert space. In this paper, we prove that an operator T acting on H is a norm limit of those operators with single-valued extension property (SVEP for short) if and only if T?, the adjoint of T, is quasitriangular. Moreover, if T? is quasitriangular, then, given an ε>0, there exists a compact operator K on H with ‖K‖<ε such that T+K has SVEP. Also, we investigate the stability of SVEP under (small) compact perturbations. We characterize those operators for which SVEP is stable under (small) compact perturbations. |
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Keywords: | Single-valued extension property Compact perturbation |
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