Generalized Daugavet equations and invertible operators on uniformly convex Banach spaces
The author introduces and investigates a generalized Daugavet equation \(|I+S+T|=1+|S|+|T|\) for operators \(S,T\) in a uniform convex Banach space. This extends the Daugavet equation \(|I+S|=1+|S|\). The author gives several characterizations for a couple \(S,T\) to be a solution of the generalized Daugavet equation. For instance, this is equivalent to the fact that the operator \((|S|+|T|)I-(S+T)\) is not invertible.
scientific article; zbMATH DE number 902456