A local spectral theory for operators. V. Spectral subspaces for hyponormal operators

Abstract

In the first part of the paper we show that the local resolvent of a hyponormal operator satisfies a rather stringent growth condition. This result enables one to show that under a mild restriction, hyponormal operators satisfy Dunford’s C condition. This in turn leads to a number of corollaries concerning invariant subspaces. In the second part we consider the local spectrum of a subnormal operator. The third section is concerned with the study of quasi-triangular hyponormal operators.