The N\"{o}rlund operator on $\ell^2$ generated by the sequence of positive integers is hyponormal

Abstract

First it is shown that the Nörlund matrix associated with the sequence of positive integers is a coposinormal operator on $\ell^2$. This fact then turns out to be useful for showing that this operator is also posinormal and hyponormal. In contrast with the analogous weighted mean matrix result [\textbf{6}], the proof of hyponormality is accomplished without resorting to determinants or Sylvester's criterion.