On N Quasi D-Operator Operators

Abstract

: In this paper, we introduce the class of N quasi D-operator acting on the usual Hilbert space H over the complex plane. An operator T is said to be an N quasi D-operator if T(T ∗2 (T D) 2 ) = N(T ∗T D) 2T, where N is a bounded operator on H. We investigate the basic behavior of this class of operator.