Arens regularity of weakly sequentially complete Banach algebras. (English) Zbl 0930.46046

Ülger, A.

Proc. Am. Math. Soc. 127, No. 11, 3221-3227 (1999).

Let \(A\) be a nonunital Banach algebra with a bounded approximate identity. It is proved that \(A\) is Arens regular if and only if it is semisimple and finite-dimensional. The paper also contains application of this result to the study of homomorphisms between Banach algebras.

Reviewer: Ismat Beg (Kuwait)

MSC:

46H10	Ideals and subalgebras
46H20	Structure, classification of topological algebras

Keywords:

nonunital Banach algebra; bounded approximate identity; Arens regular; semisimple; homomorphisms between Banach algebras