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LEFT ℓ1-FACTORABLE POLYNOMIALS
Published online by Cambridge University Press: 01 September 2009
Abstract
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.
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- Research Article
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- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2009
References
REFERENCES
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