Remarks on the second duals of Banach algebras. (English) Zbl 0572.46044

Pym, John

J. Niger. Math. Soc. 2, 31-33 (1983).

In this brief paper, an easy example is given of an Arens regular Banach algebra whose second dual is not Arens regular [an earlier example, N. J. Young, Proc. Edinburgh Math. Soc., II. Ser. 20, 99-120 (1976; Zbl 0331.46042) was quite difficult to construct]. As part of the proof, it is shown that the direct product of a sequence of regular Banach algebras need not be regular.

MSC:

46H05

General theory of topological algebras

Keywords:

Arens regular Banach algebra whose second dual is not Arens regular; the direct product of a sequence of regular Banach algebras need not be regular

Citations:

Zbl 0331.46042