Some connections between an operator and its aluthge transform

Abstract

Associated with T = U|T| (polar decomposition) in ℒ(H) is a related operator T̃ = |T| 1/2 U|T| 1/2, called the Aluthge transform of T. In this paper we study some connections between T and T̃, including the following relations; the single valued extension property, an analogue of the single valued extension property on W m(D, H), Dunford's property (C) and the property (β).