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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Stability criterion for convolution-dominated infinite matrices
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by Qiyu Sun PDF
Proc. Amer. Math. Soc. 138 (2010), 3933-3943 Request permission

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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Additional Information
  • Qiyu Sun
  • Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
  • Email: qsun@mail.ucf.edu
  • Received by editor(s): October 14, 2008
  • Received by editor(s) in revised form: November 30, 2009
  • Published electronically: July 13, 2010
  • Communicated by: Marius Junge
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 138 (2010), 3933-3943
  • MSC (2010): Primary 47B35; Secondary 40E05, 65F05, 42C40, 47G30, 94A20
  • DOI: https://doi.org/10.1090/S0002-9939-2010-10319-2
  • MathSciNet review: 2679615