A Study on Properties of skew (n,m) Binormal Operators

In this paper, the class of skew (n;m)-binormal operators acting on a Hilbert space (H) is introduced. An operator T
B(H) is skew (n,m) binormal operators if it satisfies the condition (T*mTnTnT*m)T = T(TnT*mT*mTn). We investigate some of the basic properties of this class of operators. In particular, it has been shown that any scalar multiple of a skew (n,m) binormal operator is also skew (n,m) binormal. A counter example is provided to show that the class of (n;m) binormal operators is not in general contained in the class of skew (n;m) binormal operators. The concept of (n,m)-unitary quasiequivalence is introduced and shown to be an equivalence relation. It is further shown that if an operator T is skew (n,m)-binormal, and is unitarily equivalent to an operator S, then S is also skew (n,m)-binormal.