Elementary properties of [∞,c]-symmetric operators

Abstract

Inspired by recent works on [m]-complex symmetric operator, we introduce the class of [?,C]- symmetric operators and study various properties of this class. We study the quasi-nilpotent perturbations of [?,C]-symmetric operator. Also, we prove that the class of [?,C]-symmetric operators is norm closed. Finally, we characterize when product of [?,C]-symmetric operators is also [?,C]-symmetric operator.