Factorable strongly \(p\)-nuclear \(m\)-homogeneous polynomials (Q2314643)

The main objective of the present paper is the study of the class of factorable strongly \(p\)-nuclear \(m\)-linear operators and its polynomial version. For the sake of clarity, both definitions are given: for multilinear mappings and for homogeneous polynomials. The authors give some characterization of factorable strongly \(p\)-nuclear polynomials. Specifically, they prove that a polynomial \(P\) is factorable strongly \(p\)-nuclear if and only if its linearization \(P_{L}\) is \(p\)-nuclear. This result justifies the introduction of this class. The deep connection with Grothendieck-integral polynomials is also analysed.