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


Products of Cesàro convergent sequences with applications to convex solid sets and integral operators

Author: Anton R. Schep
Journal: Proc. Amer. Math. Soc. 137 (2009), 579-584
MSC (2000): Primary 40G05, 46E30, 47B34
Published electronically: August 19, 2008
MathSciNet review: 2448578
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Abstract: Let $ 0\le a_{n}, b_{n}, c_{n}$ such that $ a_{n}=b_{n}c_{n}$. If $ a=\lim_{n\to \infty}a_{n}$, and $ \{b_{n}\}$ and $ \{c_{n}\}$ Cesàro converge to $ b$, respectively $ c$, then $ a\le bc$. This implies that if in addition $ \{b_{n}\}$ and $ \{c_{n}\}$ are similarly ordered, then $ a=bc$. As applications we prove that the pointwise product of two convex solid sets closed in measure is again closed in measure and a factorization result for kernels of regular integral operators on $ L_{p}$-spaces.

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Additional Information

Anton R. Schep
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208

PII: S 0002-9939(08)09662-7
Keywords: Ces\`aro convergence, convex solid sets, integral operators
Received by editor(s): January 23, 2008
Published electronically: August 19, 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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