THE GROTHENDIECK-PIETSCH DOMINATION PRINCIPLE FOR NONLINEAR SUMMING INTEGRAL-OPERATORS

We transform the concept of p-summing operators, 1 less than or equal to p < infinity, to the more general setting of nonlinear Banach space operators. For 1-summing operators on B(Sigma, X)-spaces having weak integral representations we generalize the Grothendieck-Pietsch domina tion principle. This is applied for the characterization of 1-summing Hammerstein operators on C(S, X)-spaces. For p-summing Hammerstein ope rators we derive the existence of control measures and p-summing exten sions to B(Sigma, X)-spaces.