NEW CHARACTERIZATION FOR THE WEYL ESSENTIAL SPECTRUM OF OPERATORS

Let A be a bounded linear operator in a complex Ba- nach space X. We show that IdX - A is a Fredholm operator provided that A has a sufficiently small polynomially measure of noncompactness. In our general framework, we note that the case of Riesz operator becomes a particular one as it is for the other results in the domain. This enable us to obtain a new characteri- zation for the Weyl essential spectrum of a closed densely defined operators.