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Coincidence Results for Summing Multilinear Mappings

Part of: Measures, integration, derivative, holomorphy Special classes of linear operators

Published online by Cambridge University Press:  03 June 2016

Oscar Blasco ,
Geraldo Botelho ,
Daniel Pellegrino  and
Pilar Rueda
Oscar Blasco
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, 46.100 Burjasot, Valencia, Spain (oscar.blasco@uv.es; pilar.rueda@uv.es)
Geraldo Botelho
Affiliation:
Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902 Uberlândia, Brazil (botelho@ufu.br)
Daniel Pellegrino
Affiliation:
Departamento de Matemática, Universidade Federal da Paraíba, 58.051-900 João Pessoa, Brazil (dmpellegrino@gmail.com; pellegrino@pq.cnpq.br)
Pilar Rueda
Affiliation:
Departamento de Análisis Matemático, Universidad de Valencia, 46.100 Burjasot, Valencia, Spain (oscar.blasco@uv.es; pilar.rueda@uv.es)
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Abstract

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In this paper we prove coincidence results concerning spaces of absolutely summing multilinear mappings between Banach spaces. The nature of these results arises from two distinct approaches: the coincidence of two a priori different classes of summing multilinear mappings, and the summability of all multilinear mappings defined on products of Banach spaces. Optimal generalizations of known results are obtained. We also introduce and explore new techniques in the field: for example, a technique to extend coincidence results for linear, bilinear and even trilinear mappings to general multilinear ones.

Keywords

absolutely summingprojective tensor productCohen summingmultilinear mapping

MSC classification

Secondary: 46G25: (Spaces of) multilinear mappings, polynomials 47B10: Operators belonging to operator ideals (nuclear, $p$-summing, in the Schatten-von Neumann classes, etc.)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 4 , November 2016 , pp. 877 - 897
Copyright
Copyright © Edinburgh Mathematical Society 2016