# IJPAM: Volume 82, No. 1 (2013)

THE MAXIMALITY OF -FACTORABLE
MULTI-LINEAR OPERATORS

B.M. Cerna
Departamento de Ciencias, Escuela de Matemáticas
Universidad Nacional Santiago Antunez de Mayolo"
Avenida Centenario 100, Huaraz, PERU

Abstract. This work demostrate the equivalence of the following definitions let is called factorable, if exist a measure space and operators and such that .

The collection of the -factorable multi-linear operators of to will be denoted for . Also , where the infimun is taken over all possible factorzation of is a norm over , '' and let .

A operator is called -factorable relative to if belongs to the normed ideal:

such that , with norm

where the supremun is taken on all the with and such that , ''.

AMS Subject Classification: 47H60, 46G25, 47L20

Key Words and Phrases: multi-linear operators, Banach spaces, operator ideals