Polynomials with an integral representation

We introduce a large class of polynomials between Banach spaces which admit an integral representation. This class coincides with the class of integral polynomials in the scalar-valued case, but it is larger in the vector-valued case. By comparing this class with other well-known classes, we obtain characterizations of Banach spaces containing no copy of co, of Grothendieck spaces, and of L-infinity-spaces. Among some other results, we show that a polynomial has an integral representation if and only if it admits an orthogonally additive extension to C (B-E*). Moreover, if the range space is complemented in its bidual, every polynomial with an integral representation is extendible to every superspace. (C) 2017 Elsevier Inc. All rights reserved.