Abstract

Let $H$ be a Hilbert space. In this paper we give a necessary and  sufficient condition for a  $lambdainmathbb{C}$ to be  an eigenvalue of the linear operator $T=D+sum_{i=1}^{n}u_iotimes v_i$, where $D$ is a diagonalizable operator and $u_i, v_iin H$, $i=1,ldots,n$.