Operators which Factor through Convex Banach Lattices

Reisner, Shlomo

Canadian journal of mathematics, Tome 32 (1980) no. 6, pp. 1482-1500

Résumé

We investigate here classes of operators T between Banach spaces E and F, which have factorization of the form where L is a Banach lattice, V is a p-convex operator, U is a q-concave operator (definitions below) and jF is the cannonical embedding of F in F”. We show that for fixed p, q this class forms a perfect normed ideal of operators M p, q, generalizing the ideal I p,q of [5]. We prove (Proposition 5) that M p, q may be characterized by factorization through p-convex and q-concave Banach lattices. We use this fact together with a variant of the complex interpolation method introduced in [1], to show that an operator which belongs to M p, q may be factored through a Banach lattice with modulus of uniform convexity (uniform smoothness) of power type arbitrarily close to q (to p). This last result yields similar geometric properties in subspaces of spaces having G.L. – l.u.st.

Détail

DOI : 10.4153/CJM-1980-117-5

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