Numerical range of Aluthge transform of operator

Abstract

For any operator A on a Hilbert space, let (A) over tilde denote its Aluthge transform. In this paper, we prove that the closure of the numerical range of (A) over tilde is always contained in that of A. This supplements the recently proved case for dim ker A less than or equal to dim ker A* by Yamazaki, and partially confirms a conjecture of Jung, Ko and Pearcy. (C) 2002 Elsevier Science Inc. All rights reserved.