Square roots of semihyponormal operators have scalar extensions

Abstract

In this paper, we study some properties of (SH), i.e., square roots of semihyponormal operators. In particular we show that an operator T∈(SH) has a scalar extension, i.e., is similar to the restriction to an invariant subspace of a (generalized) scalar operator (in the sense of Colojoara-Foiaş). As a corollary, we obtain that an operator T∈(SH) has a nontrivial invariant subspace if its spectrum has interior in the plane. © 2003 Éditions scientifiques et médicales Elsevier SAS. All rights reserved.