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

Uniform approximation on ideals of multilinear mappings