Eskandari, R.; Mirzapour, F. On finite rank perturbation of diagonalizable operators. (English) Zbl 1352.47014 Funct. Anal. Approx. Comput. 6, No. 1, 49-53 (2014). 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 Keywords:hyperinvariant subspace; matrix operator; finite rank perturbation PDFBibTeX XMLCite \textit{R. Eskandari} and \textit{F. Mirzapour}, Funct. Anal. Approx. Comput. 6, No. 1, 49--53 (2014; Zbl 1352.47014) Full Text: Link