  Every absolutely summing linear operator is weakly compact. However, for
strongly summing multilinear operators and polynomials - one of the most
natural extensions of the linear case to the non linear framework - weak
compactness does not hold in general. We show that a subclass of the class of
strongly summing multilinear operators/polynomials, sharing its main properties
such as Grothendieck's Theorem, Pietsch Domination Theorem and Dvoretzky-Rogers
Theorem, has even better properties like weak compactness and a natural
factorization theorem.
