Lipschitz Grothendieck-integral operators

Abstract

Let X be a pointed metric space and let E be a Banach space. It is known that the Lipschitz space Lip0(X,E*) is isometrically isomorphic to (F(X)⊗πE)*, the dual of the projective tensor product of the Lipschitz-free space F(X) and E. Since the injective norm ε on F(X)⊗E is smaller than the projective norm π, we study Lipschitz Grothendieck-integral operators which are exactly those elements in Lip0(X,E*) which correspond to the elements of (F(X)⊗ε E)*, the dual of the injective tensor product of F(X) and E.