On ultra-products of some families of composition operators between certain finite dimensional ℓp spaces

Let 0 and lt; σ and lt; 1 and 1 and lt; p, r and lt; ∞ be such that 1/r + (1- σ)/p' = 1. We show that for every continuous linear map T between Banach spaces E, F such that its restriction to every finite dimensional subspace N of E factorizes through a chain of type ℓ∞ (ΩN,μN) → ℓr ∞ (ΩN,μN)...