On Relation between the Joint Essential Spectrum and the Joint Essential Numerical Range of Aluthge Transform
O. S. Cyprian *
Department of Mathematics, South Eastern Kenya University, P.O.Box 170-90200, Kitui, Kenya.
*Author to whom correspondence should be addressed.
Abstract
Associated with every commuting m-tuples of operators on a complex Hilbert space X is its Aluthge transform. In this paper we show that every commuting m-tuples of operators on a complex Hilbert space X and its Aluthge transform have the same joint essential spectrum. Further, it is shown that the joint essential spectrum of Aluthge transform is contained in the joint essential numerical range of Aluthge transform.
Keywords: Aluthge transform, joint essential spectrum, joint essential numerical range