Cotype and nonlinear absolutely summing mappings

In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every \(n\)% -linear mapping from \(\mathcal{L}_{\infty}\)-spaces into \(\mathbb{K}\) is \(% (2;2,...,2,\infty)\)-summing and also shown that every \(n\)-linear...

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Bibliographic Details
Published in:arXiv.org 2003-07
Main Author: Pellegrino, Daniel M
Format: Article
Language:English
Subjects:
Banach spaces
Domains
Mapping
Polynomials
Online Access:Get full text
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Summary:In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every \(n\)% -linear mapping from \(\mathcal{L}_{\infty}\)-spaces into \(\mathbb{K}\) is \(% (2;2,...,2,\infty)\)-summing and also shown that every \(n\)-linear mapping from \(\mathcal{L}_{\infty}\)-spaces into \(F\) is \((q;2,...,2)\)-summing whenever \(F\) has cotype \(q.\) We also give new examples of analytic summing mappings and polynomial and multilinear versions of a linear Extrapolation Theorem.
ISSN:2331-8422