Stability Criterion for Convolution-Dominated Infinite Matrices

TL;DR

This paper establishes a practical criterion to determine the $ ext{l}^p$-stability of convolution-dominated infinite matrices, which is crucial for understanding their boundedness and invertibility on sequence spaces.

Contribution

The paper introduces a new, practical criterion for assessing the $ ext{l}^p$-stability of convolution-dominated infinite matrices, advancing theoretical understanding.

Findings

Provides a criterion for $ ext{l}^p$-stability

Ensures boundedness and invertibility of matrices

Applicable to convolution-dominated matrices

Abstract

Let $\ell^p$ be the space of all $p$-summable sequences on $\mathbb{Z}$. An infinite matrix is said to have $\ell^p$-stability if it is bounded and has bounded inverse on $\ell^p$. In this paper, a practical criterion is established for the $\ell^p$-stability of convolution-dominated infinite matrices.