## Distinguishing properties of Arens irregularity

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- by Zhiguo Hu and Matthias Neufang
- Proc. Amer. Math. Soc.
**137**(2009), 1753-1761 - DOI: https://doi.org/10.1090/S0002-9939-08-09678-0
- Published electronically: 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.## References

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## Bibliographic 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