Approximate Identity and Arens Regularity of Some Banach Algebras

Kazem Haghnejad Azar, Abdolhamid Riazi

Let $A$ be a Banach algebra with the second dual $A^{\ast \ast }$. If $A$ has a bounded approximate identity $(=BAI)$, then $A^{\ast \ast }$ is unital if and only if $A^{\ast \ast }$ has a $weak^* bounded…