On Analytic Roots of Hyponormal Operators

Abstract

In this paper, we provide a condition under which analytic roots of hyponormal operators (defined below) have scalar extensions. As an application, we show that such analytic roots of hyponormal operators have nontrivial hyperinvariant subspaces. We also give some structures for analytic roots of hyponormal operators. Finally, we verify that the product of some analytic root of a hyponormal operator and an algebraic operator which are commuting is subscalar. © 2017, Springer International Publishing AG.