On the $\ell_p$ and $\ell_{p,q}$ norms of Cauchy-Toeplitz matrices

Abstract

New upper and lower bounds for the $\ell_p (1<p<\infty)$ norms of  Cauchy-Toeplitz matrices in the form $T_n=[2/(1+2(i-j))]_{i,j=1}^n$ are derived. Moreover, we give a complete answer to a conjecture proposed by D. Bozkurt.