Stability criterion for convolution-dominated infinite matrices

Sun, Qiyu

doi:10.1090/S0002-9939-2010-10319-2

Stability criterion for convolution-dominated infinite matrices
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by Qiyu Sun

Proc. Amer. Math. Soc. 138 (2010), 3933-3943

DOI: https://doi.org/10.1090/S0002-9939-2010-10319-2

Published electronically: July 13, 2010

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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.

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