Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Products of Cesàro convergent sequences with applications to convex solid sets and integral operators
HTML articles powered by AMS MathViewer

by Anton R. Schep PDF
Proc. Amer. Math. Soc. 137 (2009), 579-584 Request permission

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.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 40G05, 46E30, 47B34
  • Retrieve articles in all journals with MSC (2000): 40G05, 46E30, 47B34
Additional Information
  • Anton R. Schep
  • Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Carolina 29208
  • MR Author ID: 155835
  • Email: schep@math.sc.edu
  • Received by editor(s): January 23, 2008
  • Published electronically: August 19, 2008
  • Communicated by: Nigel J. Kalton
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 579-584
  • MSC (2000): Primary 40G05, 46E30, 47B34
  • DOI: https://doi.org/10.1090/S0002-9939-08-09662-7
  • MathSciNet review: 2448578