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arXiv · 0810.5540

Uniform approximation on ideals of multilinear mappings

Geraldo Botelho·Pablo Galindo·Leonardo Pellegrini
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Abstract

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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Geraldo Botelho, Pablo Galindo, Leonardo Pellegrini. 2008-10-30. Uniform approximation on ideals of multilinear mappings. https://arxiv.org/abs/0810.5540

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