Interpolative construction and the generalized cotype of abstract Lorentz spaces

The Banach operator ideals generated by an interpolative construction depending on concave functions are studied. These ideals are described in terms of factorization through abstract interpolation Lorentz spaces. The abstract notion of Rademacher type and cotype for operators between Banach spaces is introduced. It is shown that abstract interpolation Lorentz spaces that appeared in the factorization theorem are of the generalized Rademacher cotype determined by Orlicz sequence spaces.