SPECTRAL PROPERTIES BETWEEN OPERATOR MATRICES AND HELTON CLASS

Abstract

In this paper, we study properties of Helton class of an operator matrix. In particular, we show that some upper operator matrix belongs to Helton class of an operator matrix have the property (beta)(epsilon). As an application, we get that such operators have nontrivial invariant sub-spaces. Finally, we prove that Helton class preserves the generalized Weyl's theorem under some conditions.