SOME CONNECTIONS BETWEEN AN OPERATOR AND ITS ALUTHGE TRANSFORM

Associated with T=U|T| (polar decomposition) in L(H) is a related operator T = |T|^(1/2)U|T|^(1/2), called the Aluthge transform of T. In this paper we study some connections between T and T, including the following relations; the single valued extension property, an analogue of the single valued extension property on W^(m)(D,H), Dunfordʹs property (C) and the property (beta).