Numerical range of Aluthge transform of operator Original Research Article

For any operator A on a Hilbert space, let image denote its Aluthge transform. In this paper, we prove that the closure of the numerical range of image is always contained in that of A. This supplements the recently proved case for dimkerAless-than-or-equals, slantdimkerA* by Yamazaki, and partially confirms a conjecture of Jung, Ko and Pearcy.