0000000000282984

AUTHOR

T. W. Gamelin

showing 2 related works from this author

Fredholm composition operators on algebras of analytic functions on Banach spaces

2010

AbstractWe prove that Fredholm composition operators acting on the uniform algebra H∞(BE) of bounded analytic functions on the open unit ball of a complex Banach space E with the approximation property are invertible and arise from analytic automorphisms of the ball.

Discrete mathematicsMathematics::Functional AnalysisPure mathematicsSpectral theoryApproximation propertyFredholm operatorGlobal analytic functionFinite-rank operatorFredholm integral equationFredholm operatorCompact operatorFredholm theorysymbols.namesakesymbolsComposition operatorBounded analytic functionAnalysisMathematicsJournal of Functional Analysis
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Composition operators on uniform algebras, essential norms, and hyperbolically bounded sets

2006

Let A be a uniform algebra, and let o be a self-map of the spectrum M A of A that induces a composition operator C o 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 o . It is shown that the essential spectral radius of C o , is strictly less than 1 if and only if the image of M A under some iterate o n of o 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.

Discrete mathematicsPure mathematicsComposition operatorSpectral radiusApplied MathematicsGeneral MathematicsClopen setBounded functionUniform algebraEssential spectrumPartition (number theory)Operator normMathematicsTransactions of the American Mathematical Society
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