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Exceptional sets and Hilbert–Schmidt composition operators

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Gallardo Gutiérrez, Eva A. and González, María J. (2003) Exceptional sets and Hilbert–Schmidt composition operators. Journal of Functional Analysis, 199 (2). pp. 287-300. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S002212360200006X


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Abstract

It is shown that an analytic map phi of the unit disk into itself inducing a Hilbert-Schmidt composition operator on the Dirichlet space has the property that the set E-phi = {e(i0)is an element ofpartial derivativeD : \phi(e(10))\ = 1 has zero logarithmic capacity. We also show that this is no longer true for compact composition operators on the Dirichlet space. Moreover, such a condition is not even satisfied by Hilbert-Schmidt composition operators on the Hardy space.


Item Type:Article
Uncontrolled Keywords:Hilbert-Schmidt operator; composition operator; Dirichlet space; logarithmic capacity
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21122
Deposited On:26 Apr 2013 10:59
Last Modified:10 Aug 2018 11:03

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