Volume 36 • Number 2 • 2013   • Invariance of Arens Irregularity under Extensions Ali Reza Nooreddiny and Abdolhamid Riazi Abstract. 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 \"{U}lger. 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. 2010 Mathematics Subject Classification: Primary 46H20, 46H25; Secondary 43A20 Full text: PDF