Weighted composition operators as Daugavet centers

Romain Demazeux (1)

1 LML - Laboratoire de Mathématiques de Lens

We investigate the norm identity $\|uC_\varphi + T\| = \|u\|_\infty + \|T\|$ for classes of operators on $C(S)$, where $S$ is a compact Hausdorff space without isolated point, and characterize those weighted composition operators which satisfy this equation for every weakly compact operator $T : C(S)\rightarrow C(S)$. We also give a characterization of such weighted composition operator acting on the disk algebra $A(D).$

Keywords: Weighted composition operators; Daugavet center; Daugavet property

Domains: Mathematics [math]; Functional Analysis [math.FA]

Romain Demazeux. Weighted composition operators as Daugavet centers. 2009. ⟨hal-00442267⟩