Elementary Properties of [∞,C]-symmetric Operators

Abstract

Inspired by recent work 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 show that the class of [∞,C]-symmetric operators is norm closed. Finally, we characterize when product of [∞,C]-symmetric operators is also [∞,C]-symmetric operator.