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• W1592969631 abstract "Let $A$ be a uniform algebra, and let $phi$ be a self-map of the spectrum $M_A$ of $A$ that induces a composition operator $C_phi$ on $A$. The object of this paper is to relate the notion of “hyperbolic boundedness” introduced by the authors in 2004 to the essential spectrum of $C_phi$. It is shown that the essential spectral radius of $C_phi$ is strictly less than $1$ if and only if the image of $M_A$ under some iterate $phi ^n$ of $phi$ is hyperbolically bounded. The set of composition operators is partitioned into “hyperbolic vicinities that are clopen with respect to the essential operator norm. This partition is related to the analogous partition with respect to the uniform operator norm." @default.
• W1592969631 created "2016-06-24" @default.
• W1592969631 creator A5005754129 @default.
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• W1592969631 date "2006-11-22" @default.
• W1592969631 modified "2023-09-24" @default.
• W1592969631 title "Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets" @default.
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• W1592969631 doi "https://doi.org/10.1090/s0002-9947-06-04098-0" @default.
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