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Abstract: We investigate the norm identity $\|uC \phi + T\| = \|u\| \infty + \|T\|$ forclasses of operators on $CS$, where $S$ is a compact Hausdorff space withoutisolated point, and characterize those weighted composition operators whichsatisfy this equation for every weakly compact operator $T : CS\to CS$. Wealso give a characterization of such weighted composition operator acting onthe disk algebra $AD.$



Author: Romain Demazeux LML

Source: https://arxiv.org/



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