Hyponormality of Generalized Cesàro Matrices of Every Positive Integer Order

For a positive integer $m$ and a real parameter $α>-1$, consider the generalized Cesàro matrix on $\ell^2(\mathbb N_0)$ with entries $m(n-j+1)_{m-1}/(n+α+1)_m$ for $j\le n$. We give a computer-assisted proof that this operator is hyponormal if and only if $α\ge0$. The main algebraic ingredient is an