Supraposinormality and hyponormality for the generalized Ces\`aro matrices of order two

Abstract

It is well known that the generalized Ces\`aro matrices of order one are hyponormal operators on $\ell^2$, and it has recently been shown that the Ces\`aro matrix of order two is also hyponormal. Here the relatively new concept of supraposinormality is used to show that the generalized Ces\`aro matrices of order two are both posinormal and coposinormal, and that "most" of them are also hyponormal. A conjecture is propounded that would extend the hyponormality result.