L. Najarpisheh
Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran.
[ 1 ] - Arens regularity of bilinear maps and Banach modules actions
Let $X$, $Y$ and $Z$ be Banach spaces and $f:Xtimes Y longrightarrow Z$ a bounded bilinear map. In this paper we study the relation between Arens regularity of $f$ and the reflexivity of $Y$. We also give some conditions under which the Arens regularity of a Banach algebra $A$ implies the Arens regularity of certain Banach right module action of $A$ .
[ 2 ] - Arens regularity and derivations of Hilbert modules with the certain product
Let $A$ be a $C^*$-algebra and $E$ be a left Hilbert $A$-module. In this paper we define a product on $E$ that making it into a Banach algebra and show that under the certain conditions $E$ is Arens regular. We also study the relationship between derivations of $A$ and $E$.