Strongly approximative similarity of operators

Abstract

For the bounded linear operators acting on a complex separable Hilbert space H, we introduce a binary relation ∼ sas called strongly approximative similarity. It lies between the similarity and the essential similarity. For a class of biquasitriangular operators and a class of quasitriangular operators, this relation is characterized respectively. As a result, the relation ∼ sas is an equivalent relation in this two cases.