  For each ideal of multilinear mappings $\cal M$ we explicitly construct a
corresponding ideal $^{a}{\cal M}$ such that multilinear forms in $^{a}{\cal
M}$ are exactly those which can be approximated, in the uniform norm, by
multilinear forms in ${\cal M}$. This construction is then applied to finite
type, compact, weakly compact and absolutely summing multilinear mappings. It
is also proved that the correspondence ${\cal M} \mapsto ^{a}{\cal M}$ is
Aron-Berner stability preserving.
