On Rank One Perturbations of Complex Symmetric Operators

Eungil Ko, Ji Eun Lee

In this paper we study the decomposability of rank one perturbations of complex symmetric operators $R=T+u\otimes v$. Also we investigate some conditions for which $R$ satisfies $a$-Weyl's theorem. Finally, we characterize some conditions for $R$ to be hyponormal. As consequences, we provide several cases for such operators.