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On finite rank perturbation of diagonalizable operators. (English) Zbl 1352.47014

Summary: Let \(H\) be a Hilbert space. In this paper we give a necessary and sufficient condition for a \(\lambda \in\mathbb C\) to be an eigenvalue of the linear operator \(T=D+\sum^n_{i=1} u_i \otimes v_i\), where \(D\) is a diagonalizable operator and \(u_i\), \(v_i \in H\), \(i=1,\dots,n\).

MSC:

47A55 Perturbation theory of linear operators
47A15 Invariant subspaces of linear operators
47B07 Linear operators defined by compactness properties
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