Dominated, diagonal polynomials on ? p spaces

摘要

We show that the r-dominated polynomials on ℓ p (2 ≦ p ≦ ∞) are integral on ℓ1, and give examples proving that the converse is not true. We characterize when the 2-homogeneous, diagonal polynomials on ℓ p (1 < p ≦ ∞) are r-dominated. We prove that, unlike the linear case, there are nuclear polynomials which are not 1-dominated.