Distinguishing properties of Arens irregularity
Proceedings of the American Mathematical Society , Volume 137 - Issue 5 p. 1753- 1761
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.
|Arens products, Banach algebras, Fourier algebras, Topological centres, Weakly almost periodic functionals|
|Proceedings of the American Mathematical Society|
|Organisation||School of Mathematics and Statistics|
Hu, Z. (Zhiguo), & Neufang, M. (2009). Distinguishing properties of Arens irregularity. Proceedings of the American Mathematical Society, 137(5), 1753–1761. doi:10.1090/S0002-9939-08-09678-0