Geodesic
LEFT l1-FACTORABLE POLYNOMIALS
Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 631-649

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DOI

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.
DOI : 10.1017/S001708950999005X
Mots-clés : Primary 46G25, secondary 47H60, 46B20, 46B22 
CILIA, RAFFAELLA; GUTIÉRREZ, JOAQUÍN M. LEFT l1-FACTORABLE POLYNOMIALS. Glasgow mathematical journal, Tome 51 (2009) no. 3, pp. 631-649. doi: 10.1017/S001708950999005X
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     title = {LEFT {l1-FACTORABLE} {POLYNOMIALS}},
     journal = {Glasgow mathematical journal},
     pages = {631--649},
     year = {2009},
     volume = {51},
     number = {3},
     doi = {10.1017/S001708950999005X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708950999005X/}
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