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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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Distinguishing properties of Arens irregularity
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by Zhiguo Hu and Matthias Neufang PDF
Proc. Amer. Math. Soc. 137 (2009), 1753-1761 Request permission

Abstract:

In this paper, we present a number of examples of commutative Banach algebras with various Arens irregularity properties. These examples illustrate in particular that strong Arens irregularity and extreme non-Arens regularity, the two natural concepts of “maximal” Arens irregularity for general Banach algebras as introduced by Dales-Lau and Granirer, respectively, are indeed distinct. Thereby, an open question raised by several authors is answered. We also link these two properties to another natural Arens irregularity property.
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Additional Information
  • Zhiguo Hu
  • Affiliation: Department of Mathematics and Statistics, University of Windsor, Windsor,Ontario, N9B 3P4, Canada
  • Email: zhiguohu@uwindsor.ca
  • Matthias Neufang
  • Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario,K1S 5B6, Canada
  • MR Author ID: 718390
  • Email: mneufang@math.carleton.ca
  • Received by editor(s): June 16, 2008
  • Published electronically: November 17, 2008
  • Additional Notes: Both authors were partially supported by NSERC
  • Communicated by: Nigel J. Kalton
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 1753-1761
  • MSC (2000): Primary 43A20, 43A30, 46H05
  • DOI: https://doi.org/10.1090/S0002-9939-08-09678-0
  • MathSciNet review: 2470834