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.
Categories: math.FA