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LEFT ℓ1-FACTORABLE POLYNOMIALS

Published online by Cambridge University Press:  01 September 2009

RAFFAELLA CILIA  and
JOAQUÍN M. GUTIÉRREZ
RAFFAELLA CILIA
Affiliation:
Dipartimento di Matematica, Facoltà di Scienze, Università di Catania, Viale Andrea Doria 6, 95125 Catania, Italy e-mail: cilia@dmi.unict.it
JOAQUÍN M. GUTIÉRREZ
Affiliation:
Departamento de Matemática Aplicada, ETS de Ingenieros Industriales, Universidad Politécnica de Madrid, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain e-mail: jgutierrez@etsii.upm.es
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Abstract

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A polynomial P ∈ (kE, F) is left ℓ1-factorable if there are a polynomial Q ∈ (kE, ℓ1) and an operator L ∈ (ℓ1, F) such that P = L ○ Q. We characterise the Radon–Nikodým property by the left ℓ1-factorisation of polynomials on L1(μ). We study the left ℓ1-factorisation of nuclear, compact and Pietsch integral polynomials. For Pietsch integral polynomials, we introduce the left integral ℓ1-factorisation property, obtaining a second polynomial characterisation of the Radon–Nikodým property and showing that it plays a role somehow comparable, in this setting, to nuclearity of operators. A characterisation of 1-spaces is also given in terms of the left compact ℓ1-factorisation of polynomials.

Keywords

Primary 46G25secondary 47H6046B2046B22
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 631 - 649
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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