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Spectrum of compact weighted composition operators on the weighted Hardy space in the unit ball.

Zhou, Ze-Hua; Yuan, Cheng — 2007

Journal of Inequalities and Applications [electronic only]

Spectra of weighted composition operators on algebras of analytic functions on Banach spaces

Cheng Yuan; Ze-Hua Zhou — 2011

Czechoslovak Mathematical Journal

Let $E$ be a complex Banach space, with the unit ball $B_{E}$ . We study the spectrum of a bounded weighted composition operator $u C_{ϕ}$ on $H^{\infty} (B_{E})$ determined by an analytic symbol $ϕ$ with a fixed point in $B_{E}$ such that $ϕ (B_{E})$ is a relatively compact subset of $E$ , where $u$ is an analytic function on $B_{E}$ .

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