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THE ESSENTIAL NORM OF A WEIGHTED COMPOSITION OPERATOR FROM THE BLOCH SPACE TO H∞

Part of: Special classes of linear operators

Published online by Cambridge University Press:  05 May 2009

TAKUYA HOSOKAWA
TAKUYA HOSOKAWA*
Affiliation:
Institute of Basic Science, Korea University, Seoul, 136-713, Korea (email: [email protected])
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Abstract

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We express the operator norm of a weighted composition operator which acts from the Bloch space ℬ to H∞ as the supremum of a quantity involving the weight function, the inducing self-map, and the hyperbolic distance. We also express the essential norm of a weighted composition operator from ℬ to H∞ as the asymptotic upper bound of the same quantity. Moreover we study the estimate of the essential norm of a weighted composition operator from H∞ to itself.

Keywords

weighted composition operatorthe space of bounded analytic functionsBloch space

MSC classification

Secondary: 47B33: Composition operators
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 79 , Issue 3 , June 2009 , pp. 487 - 497
Copyright
Copyright © Australian Mathematical Society 2009

Footnotes

This work was supported by the Korean Research Foundation Grant funded by Korean Government (KRF-2008-314-C00012).

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