Dominated, diagonal polynomials on ℓp spaces
We show that the r-dominated polynomials on ℓp(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 ℓp(1 < p ≦ ∞) are r-dominated. We prove that, unlike the linear case, there are nuclear polynomials which are not 1-dominated.
Mathematics Subject Classification (2000).Primary 46G25 Secondary 47H60
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