On the Arens regularity of a module action and its extensions

Document Type: Original Article

Author

Department of Mathematics, University of Bojnord, P.O. Box 1339, Bojnord, Iran.

10.22034/kjm.2020.109816

Abstract

It is known  that if the second dual $A^{**}$ of a Banach algebra $A$ is Arens regular, then  $A$ is Arens regular itself. However, the converse is not true, in general. Young  gave an example of an Arens regular Banach algebra whose second dual is not Arens regular. Later Pym has polished Young's example  for presenting   more applicable examples. In this paper, we mimic the methods of Young and Pym to present  examples of some  Arens regular bilinear maps  and module actions whose  some extensions are not Arens regular.
 Finally, some relationships between the topological centers of certain Banach module actions are investigated.

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