Essential spectrum of the products of operators
Xiaohong Cao · Journal of Shandong University · 2010
Let A be a bounded linear operator on a Hilbert space H.A∈B(H) is called a consistent in Fredholm(briefly CF operator) or A has property CF if σe(AB)=σe(BA) for every B∈B(H),where σe(·) denotes the essential spectrum.In this note,sufficient and necessary conditions for property CF are given,and the property CF for compact perturbation of A is considered.Finally,the properties CF of operator matrices are studied.