Hyponormality-Preserving Finite Rank Perturbations Of Terraced Matrices

Abstract

Suppose M is a terraced matrix that is a hyponormal bounded linear operator on l2. Here we determine conditions under which there exists a finite rank terraced matrix F =/= 0 such that M + F is also hyponormal. Two different approaches are employed. One approach uses Sylvester’s criterion, and the other uses the recently defined concept of supraposinormality. Examples include generalized Cesaro operators of order one and terraced matrices associated with some logistic sequences.