LEFT ℓ1-FACTORABLE POLYNOMIALS.

Authors :: Cilia, Raffaella
Gutiérrez, Joaquín M.
Source :: Glasgow Mathematical Journal; Sep2009, Vol. 51 Issue 3, p631-649, 19p
Publication Year :: 2009
Abstract: ApolynomialP ϵ P(<superscript>k</superscript>E, F) is left ℓ<subscript>1</subscript>-factorable if there are a polynomial Q ϵ P(<superscript>k</superscript>E, ℓ<subscript>1</subscript>) and an operator L ϵ L(ℓ<subscript>1</subscript>, F) such that P = L o Q. We characterise the Radon-Nikodým property by the left ℓ<subscript>1</subscript>-factorisation of polynomials on L<subscript>1</subscript>(μ). We study the left ℓ1-factorisation of nuclear, compact and Pietsch integral polynomials. For Pietsch integral polynomials, we introduce the left integral ℓ<subscript>1</subscript>-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 ℒ<subscript>1</subscript>-spaces is also given in terms of the left compact ℓ<subscript>1</subscript>-factorisation of polynomials. [ABSTRACT FROM AUTHOR]