It is shown that in a Grothendieck space with the Dunford-Pettis property, the class of well-bounded operators of type (B) coincides with the class of scalar-type spectral operators with real spectrum. It turns out that in such Banach spaces, analogues of the classical theorems of Hille-Sz. Nagy and Stone concerned with the integral representation of \(C_ 0\)-semigroups of normal operators and strongly continuous unitary groups in Hilbert spaces, respectively, are of a very special nature.