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The numerical range of a composition operator with conformal automorphism symbol

โœ Scribed by A. Abdollahi

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
221 KB
Volume
408
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

Let p โˆˆ U, ฮฑ p (z) := p-z 1-pz (z โˆˆ U) and let C ฮฑ p : H 2 โ†’ H 2 be the composition operator induced by the conformal automorphism ฮฑ p . In this paper we show that the closure of the numerical range of C ฮฑ p , W (C ฮฑ p ), is an ellipse with foci at ยฑ1 and major axis 2 โˆš 1-|p| 2 .

๐Ÿ“œ SIMILAR VOLUMES

The Numerical Ranges of Automorphic Comp
The Numerical Ranges of Automorphic Composition Operators
โœ Paul S. Bourdon; Joel H. Shapiro ๐Ÿ“‚ Article ๐Ÿ“… 2000 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 136 KB

We investigate the shape of the numerical range for composition operators induced on the Hardy space H 2 by conformal automorphisms of the unit disc. We show that usually, but not always, such operators have numerical ranges whose closures are discs centered at the origin. Surprising open questions