This is an announcement for the paper "On the interplay between different summability properties of multilinear mappings" by Oscar Blasco, Geraldo Botelho, Daniel Pellegrino and Pilar Rueda.
Abstract: 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.
Archive classification: math.FA
Remarks: 27 pages
Submitted from: dmpellegrino@gmail.com
The paper may be downloaded from the archive by web browser from URL
http://front.math.ucdavis.edu/1103.4040
or