The Daugavet equation for Lipschitz operators
By Dirk Werner
Also appears in collection : Exposés de recherche
We study the Daugavet equation $\parallel Id+T\parallel$ $=1$ $+$ $\parallel T\parallel$ for Lipschitz operators on a Banach space. For this we introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators to the non-linear case.