Unitary equivalence of one-parameter groups of Toeplitz and composition operators |
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| Authors: | Carl C Cowen Eva A Gallardo-Gutiérrez |
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| Institution: | a Department of Mathematical Sciences, Indiana University-Purdue University Indianapolis, Indianapolis, IN 46202, USA
b Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid, Spain |
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| Abstract: | The composition operators on H2 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 zH2 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 H2, but there is a similarity between them. |
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| Keywords: | Composition operator Toeplitz operator Subnormal operator Unitary equivalence |
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