Characterization of the matrix whose norm is determined by its action on decreasing sequences

TL;DR

This paper characterizes non-negative matrices whose operator norms are fully determined by their effects on decreasing sequences within certain normed sequence spaces, providing a deeper understanding of their structure.

Contribution

It offers a complete characterization of matrices for which the norm is determined by decreasing sequences, advancing the theory of operators on sequence spaces.

Findings

Identifies conditions under which matrix norms are determined by decreasing sequences

Provides a characterization applicable to various normed Riesz spaces

Enhances understanding of operator behavior on sequence spaces

Abstract

Let $A=(a_{j,k})_{j,k \ge 1}$ be a non-negative matrix. In this paper, we characterize those $A$ for which $\|A\|_{E, F}$ are determined by their actions on decreasing sequences, where $E$ and $F$ are suitable normed Riesz spaces of sequences.