Narrow operators on vector-valued sup-normed spaces
Narrow operators on vector-valued sup-normed spaces
We characterise narrow and strong Daugavet operators on $C(K,E)$-spaces; these are in a way the largest sensible classes of operators for which the norm equation $\|\mathrm{Id}+T\| = 1+\|T\|$ is valid. For certain separable range spaces $E$, including all finite-dimensional spaces and all locally uniformly convex spaces, we show that an …