Invariance of Arens Irregularity under Extensions

Let m be a bounded bilinear mapping on Banach spaces. First we give a sufficient condition for strong irregularity of m and apply the result to extend some earlier results by Ulger. Next, we study invariance of irregularity for m under extension of its domain from left or right. As a consequence, we improve some known results about Arens regularity. Finally, we investigate invariance of irregularity for direct sum of a family of Banach algebras.