Ideal of multilinear \({\mathcal {F}}_{\vec {p},\vec {q}}\,\)-factorable operators and applications

Abstract

In the present paper we introduce a method for generating ideals of linear and multilinear operators from what we call generalized left and right operator ideals, that we discuss with p-th power factorable, p-convex and q-concave operators. Then we combine this method with the Factorization Ideal method, that construct multilinear operators, in order to introduce the ideal of multilinear \({\mathcal {F}}_{\vec {p},\vec {q}}\)-factorable operators as an example of an ideal generated by means of our method. Finally, we investigate its relation with multilinear summing operators.