Weighted composition operators as Daugavet centers

Abstract : 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 $A(D).$
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https://hal-univ-artois.archives-ouvertes.fr/hal-00442267
Contributor : Romain Demazeux <>
Submitted on : Friday, December 18, 2009 - 9:22:39 PM
Last modification on : Sunday, December 20, 2009 - 6:30:19 PM
Long-term archiving on : Thursday, June 17, 2010 - 10:03:37 PM

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  • HAL Id : hal-00442267, version 1
  • ARXIV : 0912.4032

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

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