On operators satisfying T* T2 T T* T 2T

Let T be a bounded linear operator on a complex Hilbert space . In this paper we introduce the class, denoted , of operators satisfying T* T2 T T* T 2T and we prove basic structural properties of these operators. Using these results, we also prove that if E is the Riesz idempotent for a non-zero isolated point λ of the spectrum of , then E is self-adjoint, and we give a necessary and sufficient condition for T S to be in when T and S are both non-zero operators.