P*-Skew-Bi-Normal Operator on Hilbert Space

Abstract

In this paper we introduce an operator on Hilbert space H called P^*-skew-bi-normal operator. An operator L is called P^*-skew-bi-normal operator if and only if (L^* LLL^* ) 〖〖(L〗^*)〗^P=〖〖(L〗^*)〗^P (〖LL〗^* L^* L), where Ρ is a nonnegative integer. New theorems and properties are given on Hilbert space H.