# 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 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. 201–208

DOI 10.2977/PRIMS/6