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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability criterion for convolution-dominated infinite matrices


Author: Qiyu Sun
Journal: Proc. Amer. Math. Soc. 138 (2010), 3933-3943
MSC (2010): Primary 47B35; Secondary 40E05, 65F05, 42C40, 47G30, 94A20
Published electronically: July 13, 2010
MathSciNet review: 2679615
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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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Additional Information

Qiyu Sun
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
Email: qsun@mail.ucf.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10319-2
PII: S 0002-9939(2010)10319-2
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.