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Distinguishing properties of Arens irregularity

Authors: Zhiguo Hu and Matthias Neufang
Journal: Proc. Amer. Math. Soc. 137 (2009), 1753-1761
MSC (2000): Primary 43A20, 43A30, 46H05
Published electronically: November 17, 2008
MathSciNet review: 2470834
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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

Matthias Neufang
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario,K1S 5B6, Canada

Keywords: Banach algebras, Arens products, topological centres, weakly almost periodic functionals, Fourier algebras.
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
Article copyright: © Copyright 2008 American Mathematical Society

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