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\begin{document}
\title{Module Amenability of Banach Algebras}
\author{M. Ramezanpour}
\date{}
\maketitle
\section{Introduction and some Preliminaries}
For a Banach algebra $A$ with a bounded approximate identity, we investigate  the  $A$-module homomorphisms of certain introverted subspaces of $A^*$,  and  show that  all  $A$-module homomorphisms of $A^*$ are  normal if and only if $A$ is an ideal of $A^{**}$. We obtain some characterizations of compactness and discreteness for a locally compact quantum group $\mathbb{G}$.
$$f(x)=\mathbb{G}\Gamma(x)+\xi^x+2^x-\gamma$$
\end{document}