Dominated Bilinear Forms and 2-homogeneous Polynomials

Abstract

The main goal of this note is to establish a connection between the cotype of the Banach space X and the parameters r for which every 2-homogeneous polynomial on X is r-dominated. Let cot X be the infimum of the cotypes assumed by X and (cot X)* be its conjugate. The main result of this note asserts that if cot X > 2, then for every 1 ≤ r < (cot X)* there exists a non-r-dominated 2-homogeneous polynomial on X.