# Dominated Bilinear Forms and 2-homogeneous Polynomials

### Geraldo Botelho

Universidade Federal de Uberlândia, Brazil### Daniel Pellegrino

Universidade Federal da Paraíba, João Pessoa, Brazil### Pilar Rueda

Universitat de Valencia, Burjassot (Valencia), Spain

## 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 $cotX$ be the inﬁmum of the cotypes assumed by $X$ and $(cotX)_{∗}$ be its conjugate. The main result of this note asserts that if $cotX>2$, then for every $1≤r<(cotX)_{∗}$ 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. 201–208

DOI 10.2977/PRIMS/6