Strongly Lipschitz (ℓp ,ℓq)-factorable mappings

Abstract

In this paper we study the space of strongly Lipschitz (ℓp ,ℓq) -factorable operators between metric spaces and a Banach spaces. In particular, a factorization of this class through ℓp and ℓq spaces is given. We show that this type of operators fits in the theory of composition α-Banach Lipschitz operator ideal. As a special case, we get a Lipschitz version of weakly p-nuclear operators.

Keywords

• (p,q)-operators
• (ℓp ,ℓq)-factorable operators
• quasi (ℓp ,ℓq)-factorable operators
• ℓp-factorable operators
• strongly lipschitz (ℓp ,ℓq)-factorable operators