Proceedings of the American Mathematical Society

Author(s): Zhiguo Hu; Matthias Neufang
Journal: Proc. Amer. Math. Soc. 137 (2009), 1753-1761.
MSC (2000): Primary 43A20, 43A30, 46H05
Posted: November 17, 2008
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 43A20, 43A30, 46H05

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
Email: mneufang@math.carleton.ca

DOI: 10.1090/S0002-9939-08-09678-0
PII: S 0002-9939(08)09678-0
Keywords: Banach algebras, Arens products, topological centres, weakly almost periodic functionals, Fourier algebras.
Received by editor(s): June 16, 2008
Posted: November 17, 2008
Additional Notes: Both authors were partially supported by NSERC
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society

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