Distinguishing properties of Arens irregularity

Hu, Zhiguo; Neufang, Matthias

doi:10.1090/S0002-9939-08-09678-0

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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