Lipschitz slices and the Daugavet equation for Lipschitz operators

TL;DR

This paper introduces a new concept called Lipschitz slices for non-linear Lipschitz functionals and extends results related to the Daugavet equation from linear to non-linear operators.

Contribution

It proposes Lipschitz slices as a substitute for linear slices and transfers known linear operator results to the non-linear Lipschitz setting.

Findings

Established Lipschitz slices as a tool for non-linear analysis

Extended Daugavet equation results to Lipschitz operators

Provided new insights into non-linear operator theory

Abstract

We introduce a substitute for the concept of slice for the case of non-linear Lipschitz functionals and transfer to the non-linear case some results about the Daugavet and the alternative Daugavet equations previously known only for linear operators.