<p style='text-indent:20px;'>In this paper we look at the question of integrability, or not, two natural almost complex structures <inline-formula><tex-math id="M1">\begin{document}$ J^{\pm}_\nabla $\end{document}</tex-math></inline-formula> defined on twistor space id="M2">\begin{document}$ J(M, g) an even-dimensional manifold id="M3">\begin{document}$ M wit...

let $mathcal{a}$ be a banach algebra with bai and $e$ be an introverted subspace of $mathcal{a'}$.in this paper we study the quotient arens regularity of $mathcal{a}$ with respect to $e$ and prove that the group algebra $l^1(g)$ for a locally compact group $g$, is quotient arens regular with respect to certain introverted subspace $e$ of $l^infty(g)$.some related result are given as well.