Approximate Identity and Arens Regularity of Some Banach Algebras Kazem Haghnejad Azar and Abdolhamid Riazi
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چکیده
Let A be a Banach algebra with the second dual A∗∗. If A has a bounded approximate identity (= BAI), then A∗∗ is unital if and only if A∗∗ has a weak∗ bounded approximate identity(= W ∗BAI). If A is Arens regular and A has a BAI, then A∗ factors on both sides. In this paper we introduce new concepts LW ∗W and RW ∗W property and we show that under certain conditions if A has LW ∗W and RW ∗W property, then A is Arens regular and also if A is Arens regular, then A has LW ∗W and RW ∗W property. We also offer some applications of these new concepts for the special algebras l(G), L(G), M(G), and A(G). Mathematics Subject Classification: 46L06; 46L07; 46L10; 47L25
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