Multilinear Forms, Subsymmetric Polynomials, and Spreading Models on Banach Spaces

Abstract

Some applications of Ramsey theory to the study of multilinear forms and polynomials on Banach spaces are given, related to the existence of lowerlq-estimates of sequences. We give an explicit representation of subsymmetric polynomials in Banach spaces with subsymmetric basis. Finally we apply our results to get approximation of polynomials by subsymmetric polynomials, and to the problem of stabilization of a certain chain of algebras generated by polynomials.