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Unitary equivalence of one-parameter groups of Toeplitz and composition operators

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Gallardo Gutiérrez, Eva A. and Cowen, Carl C. (2011) Unitary equivalence of one-parameter groups of Toeplitz and composition operators. Journal of Functional Analysis, 261 (9). pp. 2641-2655. ISSN 0022-1236

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123611002588


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Abstract

The composition operators on H(2) whose symbols are hyperbolic automorphisms of the unit disk fixing +/-1 comprise a one-parameter group and the analytic Toeplitz operators coming from covering maps of annuli centered at the origin whose radii are reciprocals also form a one-parameter group. Using the eigenvectors of the composition operators and of the adjoints of the Toeplitz operators, a direct unitary equivalence is found between the restrictions to zH(2) of the group of Toeplitz operators and the group of adjoints of these composition operators. On the other hand, it is shown that there is not a unitary equivalence of the groups of Toeplitz operators and the adjoints of the composition operators on the whole of H(2), but there is a similarity between them


Item Type:Article
Uncontrolled Keywords:Composition operator; Toeplitz operator; Subnormal operator; Unitary equivalence
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:20997
Deposited On:23 Apr 2013 10:55
Last Modified:10 Aug 2018 10:48

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