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http://dx.doi.org/10.4134/JKMS.2009.46.6.1293

POLYNOMIAL FACTORIZATION THROUGH Lγ(μ) SPACES  

Cilia, Raffaella (DIPARTIMENTO DI MATEMATICA FACOLTA DI SCIENZE UNICERSITA DI CATANIA VIALE ANDREA DORIA)
Gutierrez, Joaquin M. (DEPARTAMENTO DE MATEMATICA APLICADA ETS DE INGENIEROS INDUSTRIALES UNIVERSIDAD POLITECNICA DE MADRID)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.6, 2009 , pp. 1293-1307 More about this Journal
Abstract
We give conditions so that a polynomial be factorable through an $L_{\gamma}({\mu})$ space. Among them, we prove that, given a Banach space X and an index m, every absolutely summing operator on X is 1-factorable if and only if every 1-dominated m-homogeneous polynomial on X is right 1-factorable, if and only if every 1-dominated m-homogeneous polynomial on X is left 1-factorable. As a consequence, if X has local unconditional structure, then every 1-dominated homogeneous polynomial on X is right and left 1-factorable.
Keywords
right $\gamma$-factorable polynomial; left $\gamma$-factorable polynomial; pdominated polynomial;
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