1. Distinguishing properties of Arens irregularity.
- Author
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Zhiguo Hu and Matthias Neufang
- Subjects
- *
IRREGULARITIES of distribution (Number theory) , *BANACH algebras , *COMMUTATIVE algebra , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICS - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2008
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