On Cohen almost summing multilinear operators

Abstract

We show that all Cohen strongly p-summing multilinear operators and polynomials on Banach spaces are Cohen almost summing. If the range space is a Hilbert space then all Cohen strongly p-summing multilinear operators and polynomials are strongly q-summing (1<p,q<∞). Moreover, if both domain and range spaces are Hilbert spaces then all Hilbert–Schmidt multilinear operators are Cohen strongly 2-summing.