Uniform approximation on ideals of multilinear mappings

Details Uniform approximation on ideals of multilinear mappings Uniform approximation on ideals of multilinear mappings

2008-10-30

arxiv.org/abs/0810.5540v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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.

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