Weighted composition operators as Daugavet centers

Details Weighted composition operators as Daugavet centers Weighted composition operators as Daugavet centers

2009-12-20

arxiv.org/abs/0912.4032v1

Mathematics

Functional Analysis

18 pages

Scientific paper

We investigate the norm identity $\|uC_\phi + T\| = \|u\|_\infty + \|T\|$ 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 $T : C(S)\to C(S)$. We also give a characterization of such weighted composition operator acting on the disk algebra $A(D).$

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