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

Autores: Juan Antonio López Molina , Enrique Alfonso Sánchez Pérez
Localización: Revista Colombiana de Matemáticas, ISSN-e 0034-7426, Vol. 35, Nº. 2, 2001, págs. 67-76
Idioma: inglés
Enlaces
- Texto completo
Resumen
- Let 0 < σ < 1 and 1 < p, r < ∞ 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) → ℓ 1 (ΩN,μN)+ ℓp((ΩN,μN) where (ΩN,μN) is a discrete measure space with a finite number of atoms, there is a σ- finite measure space (Ω, μ) such that T ∈ L(E, F") factorizes through the chain of "continuous spaces ℓ∞ (ΩN,μN) → ℓr ∞ (ΩN,μN) → ℓ 1 (ΩN,μN)+ ℓp((ΩN,μN)