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

TL;DR

This paper establishes new bounds for the $\, ext{ell}_p$ norms of specific Cauchy-Toeplitz matrices and resolves a conjecture related to their properties, advancing understanding in matrix norm analysis.

Contribution

It provides the first comprehensive bounds for $\, ext{ell}_p$ norms of Cauchy-Toeplitz matrices and confirms a conjecture by D. Bozkurt.

Findings

Derived new upper and lower bounds for $\, ext{ell}_p$ norms.

Resolved D. Bozkurt's conjecture on these matrices.

Enhanced understanding of matrix norm behavior.

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.