MULTILINEAR MIXING OPERATORS AND LIPSCHITZ MIXING OPERATOR IDEALS

In [15], E. A. Sanchez Perez introduced the class of (s;q,theta)-mixing operators, as a generalization of (s;q)-mixing operators. We investigate analogous concepts here for the case of multilinear operators between Banach spaces and Lipschitz mappings between metric spaces, introducing the class of (s,q;p(1),..., p(m);theta)-mixing multilinear operators and the Lipschitz Banach ideal of (s,q,theta)-mixing mappings show that our approach provides a multilinear and Lipschitz extension of quotient theorem like the linear case. Several characterizations of these mappings are presented, especially. every Lipschitz (s,q)-mixing map is Lipschitz (s,q,theta)-mixing map and a result relies on the duality theory for (q,theta)-absolutely Lipschitz operators are given.