Resumen de Multiplicative semigroups of Lipschitz functions

Félix Cabello Sánchez , Javier Cabello Sánchez

• Given a (complete) metric space X, we denote by Lip(X) the space of real-valued Lipschitz functions on X and we equip it with the pointwise product. The purpose of this note is to describe those bijections T : Lip(Y ) �¨ Lip(X) which are \multiplicative " in the sense that whenever f; g �¸ Lip(Y ) are such that fg �¸ Lip(Y ) one has T(fg) = T(f)T(g).

  The main result of the paper states that if X has no isolated points, then every mul- tiplicative bijection T : Lip(Y ) �¨ Lip(X) arises as T(f) = f .  , where  : X �¨ Y is a Lipschitz homeomorphism and so it is automatically linear.

  We also give a description of the semigroup isomo