Lip-Linear operators and their connection to Lipschitz tensor products

Abstract: The linear operators defined on the Lipschitz projective tensor product of X and E motivate the study of a distinct class of operators acting on the cartesian produc X E. This class, denoted by LipL(X E;F), combines Lipschitz and linear properties, forming an intermediate framework between bilinear operators and two-Lipschitz operators. We establish an identification between this space and L(X E;F), which also links it to the space of bilinear operators B(AE(X) E;F). Furthermore, we extend summability concepts within this category, with a particular focus on integral and dominated (p;q)-summing operators