Obiettivo
Despite extensive work in the area of un-conditionality of bases for symmetric tensor products and spaces of polynomials, certain problems remain open, for instance, when do the monomials form an unconditional basic sequence? In a recent paper it has been shown that the polynomials that admit unconditional monomial expansions can be thought of as the multi-linear analogue of the regular linear operators between Banach lattices. This fact opens up a new perspective on the area. We expect that the use of Banach lattice techniques will lead to interesting new results on un-conditionality, reflexivity, weak converge and geometry of polynomials, with all of which the project will be concerned and of which it aims to provide a better understanding.
Also the known connections between un-conditionality and local Banach space theory and several complex variables will be investigated. Undertaking the project will be beneficial both for the researcher and the host department. It will give the research team the possibility to unify a certain amount of knowledge in the area of tensor products, Schauder bases, un-conditionality and homogeneous polynomials and to achieve greater coherence in the exploration process and the exposition of results. Moreover, the project opens a new approach to the problem, which is likely to produce results of interest not only to the EU scientific community, but also to specialists in Argentina, Brazil, Israel and the USA who have already manifested interest in the area.
Parole chiave
Invito a presentare proposte
FP6-2002-MOBILITY-5
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Meccanismo di finanziamento
EIF - Marie Curie actions-Intra-European FellowshipsCoordinatore
VALENCIA
Spagna