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.
Cite this article
Geraldo Botelho, Daniel Pellegrino, Pilar Rueda, Dominated Bilinear Forms and 2-homogeneous Polynomials. Publ. Res. Inst. Math. Sci. 46 (2010), no. 1, pp. 201–208DOI 10.2977/PRIMS/6