The λ-Aluthge transform and its applications to some classes of operators

Abstract

Let T ? B(H) be a bounded linear operator on a Hilbert space H, and let T = U|T| be its polar decomposition. Then, for every ? ? [0,1] the ?-Aluthge transform of T is defined by ??(T) = |T|?U|T|1-?. In this paper, we characterize the invertible, binormal, and EP operators and its intersection with a special class of introduced operators via the ?-Aluthge transform.