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On symmetric ideals of multilinear mappings between Banach spaces

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

Published online by Cambridge University Press:  09 April 2009

Geraldo Botelho  and
Daniel M. Pellegrino
Geraldo Botelho
Affiliation:
Faculdade de Matemática, Univ. Federal de Uberlândia, 38.400-902 Uberlândia, Brazil, e-mail: [email protected]
Daniel M. Pellegrino
Affiliation:
Departamento de Matemática e Estatística, Univ. Federal de Campina Grande, 58.109-970 Campina Grande, Brazil, e-mail: [email protected]
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Abstract

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In this paper we provide examples and counterexamples of symmetric ideals of multilinear mappings between Banach spaces and prove that if I1, …, In are operator ideals, then the ideals of multilinear mappings L(I1, …, In) and /I1, …, In/ are symmetric if and only if I1 = … = In.

Keywords

Banach spacesideals of multilinear mappingsfactorization methodlinearization method.

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
Journal of the Australian Mathematical Society , Volume 81 , Issue 1 , August 2006 , pp. 141 - 148
Copyright
Copyright © Australian Mathematical Society 2006

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