On the interplay between different summability properties of multilinear mappings

Details On the interplay between different summability properties of multilinear mappings On the interplay between different summability properties of multilinear mappings

2011-03-21

arxiv.org/abs/1103.4040v1

Mathematics

Functional Analysis

27 pages

Scientific paper

In this paper we establish profitable connections between different summability properties of multilinear mappings on Banach spaces, namely, multilinear mappings that are absolutely summing, almost summing, weakly summing and Cohen summing. For example, we give techniques to extend coincidence results from linear, bilinear and, in general, n-linear mappings to m-linear mappings for m larger than n. We do so by exploring the relationships between the summability properties of an n-linear mapping with those of its associated k-linear mappings, 1 <= k < n. We also provide an optimal generalization of recent results concerning inclusion theorems for absolutely summing multilinear mappings.

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