On weighted mean matrices whose $l^p$ norms are determined on decreasing sequences

TL;DR

This paper establishes a condition under which weighted mean matrices have their $l^p$ norms determined by decreasing sequences, providing a proof of a conjecture and exploring related results.

Contribution

The paper introduces a new condition for weighted mean matrices to have $l^p$ norms determined on decreasing sequences, and proves a related conjecture.

Findings

Condition identified for weighted mean matrices' $l^p$ norms on decreasing sequences

Proof of Bennett's conjecture provided

Discussion of related results included

Abstract

We give a condition on weighted mean matrices so that their $l^p$ norms are determined on decreasing sequences when the condition is satisfied. We apply our result to give a proof of a conjecture of Bennett and discuss some related results.