Algebraic extensions of semi-hyponormal operators

Abstract

In this paper, we show that algebraic extensions of semi-hyponormal operators (defined below) are subscalar. As corollaries we get the following: (1) Every k-quasihyponormal operator is subscalar. (2) Every algebraic extension of Aluthge transforms of p-hyponormal operators is subscalar. From these results and [Es] it is known that such operators with 'rich spectra' have nontrivial invariant subspaces.