THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS

If A is a unital Banach algebra, then the spectrum can be viewed as a function sigma : A -> S, mapping each T is an element of A to its spectrum sigma(T), where S is the set, equipped with the Hausdorff metric, of all compact subsets of C. This paper is concerned with the continuity of the spectrum sigma via Browder's theorem. It is shown that sigma is continuous when sigma is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.