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Adjoints of linear fractional composition operators on the Dirichlet space

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Gallardo Gutiérrez, Eva A. and Montes Rodríguez, Alfonso (2003) Adjoints of linear fractional composition operators on the Dirichlet space. Mathematische Annalen, 327 (1). pp. 117-134. ISSN 0025-5831

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Official URL: http://link.springer.com/content/pdf/10.1007%2Fs00208-003-0442-9.pdf


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Abstract

The adjoint of a linear fractional composition operator acting on the classical Dirichlet space is expressed as another linear fractional composition operator plus a two rank operator. The key point is that, in the Dirichlet space modulo constant functions, many linear fractional composition operators are similar to multiplication operators and, thus, normal. As a particular application, we can easily deduce the spectrum of each linear fractional composition operator acting on such spaces. Even the norm of each linear fractional composition operator is computed on the Dirichlet space modulo constant functions. It is also shown that all this work can be carried out in the Hardy space of the upper half plane.


Item Type:Article
Uncontrolled Keywords:HARDY-SPACES; H-2
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:21114
Deposited On:26 Apr 2013 10:20
Last Modified:10 Aug 2018 11:37

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