On Cohen almost summing multilinear operators

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.