SOME CONNECTIONS BETWEEN AN OPERATOR AND ITS ALUTHGE TRANSFORM

摘要

Associated with T = U|T| (polar decomposition) in L(H) is a related operator (T-tilde = |T|~(1/2)U|T|~(1/2), called the Aluthge transform of T. In this paper we study some connections between T and T-tilde, 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).