Composition of operator ideals and their regular hulls

Given two quasi-Banach ideals \oid{A}{}{} and \oid{B}{}{} we investigate the regular hull of their composition - $(\oid{A}{}{} \circ \oid{B}{}{})^{reg}$. In concrete situations this regular hull appears more often than the composition itself. As a first example we obtain a description for the regular hull of the nuclear operators which is a "reflected" Grothendieck representation:\\ $\oid{N}{}{reg} \stackrel{1}{=} \oid{I}{}{} \circ \oid{W}{}{}$ (theorem 2.1). Further we recognize that the class of such ideals leads to interesting relations concerning the question of the accessibility of (injective) operator ideals.