ABSTRACT

This chapter shows attaching the open problem of the existence of an unconditional basis in spaces of m-homogeneous polynomials on infinite dimensional Banach spaces. It shows how to prove an analogue of the Pisier-Schiitt theorem for symmetric tensor products. For each m, an asymptotically optimal estimate of the unconditional basic constants of all m-homogeneous polynomials. In the purpose of studying the existence of unconditional basis in spaces of polynomials, the chapter uses some tools that come from Banach spaces theory and that are defined to provide an easier understanding of the proofs.