Proceedings of the American Mathematical Society

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Stability criterion for convolution-dominated infinite matrices

Author(s): Qiyu Sun
Journal: Proc. Amer. Math. Soc. 138 (2010), 3933-3943.
MSC (2010): Primary 47B35; Secondary 40E05, 65F05, 42C40, 47G30, 94A20
Posted: July 13, 2010
MathSciNet review: 2679615
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Abstract: Let $\ell^p$ be the space of all -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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