LEFT ℓ₁-FACTORABLE POLYNOMIALS

Abstract

We characterise the Radon-Nikodým property by the left 1 -factorisation of polynomials on L 1 (μ). We study the left 1 -factorisation of nuclear, compact and Pietsch integral polynomials. For Pietsch integral polynomials, we introduce the left integral 1 -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 1 -spaces is also given in terms of the left compact 1 -factorisation of polynomials.2000 Mathematics Subject Classification. Primary 46G25; secondary 47H60, 46B20, 46B22.