Similarity to an isometry of a composition operator
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- by Frédéric Bayart
- Proc. Amer. Math. Soc. 131 (2003), 1789-1791
- DOI: https://doi.org/10.1090/S0002-9939-02-06759-X
- Published electronically: October 1, 2002
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Abstract:
We study the composition operators which are similar to an isometry on the classical Hardy space $H^2(\mathbb {D})$.References
- Frédéric Bayart, De nouveaux espaces de séries de Dirichlet et leurs opérateurs de composition, C. R. Acad. Sci. Paris Sér. I Math. 333 (2001), no. 3, 207–212 (French, with English and French summaries). MR 1851626, DOI 10.1016/S0764-4442(01)02047-X
- Carl C. Cowen and Barbara D. MacCluer, Composition operators on spaces of analytic functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. MR 1397026
- Joseph A. Cima, James Thomson, and Warren Wogen, On some properties of composition operators, Indiana Univ. Math. J. 24 (1974/75), 215–220. MR 350487, DOI 10.1512/iumj.1974.24.24018
- Nizar Jaoua, Similarity to a contraction and hypercontractivity of composition operators, Proc. Amer. Math. Soc. 129 (2001), no. 7, 2085–2092. MR 1825921, DOI 10.1090/S0002-9939-00-05843-3
- B.Sz. Nagy, On uniformly bounded linear transformations in Hilbert space. Acta Univ. Szeged (1947)
- Eric A. Nordgren, Composition operators, Canadian J. Math. 20 (1968), 442–449. MR 223914, DOI 10.4153/CJM-1968-040-4
- Joel H. Shapiro, What do composition operators know about inner functions?, Monatsh. Math. 130 (2000), no. 1, 57–70. MR 1762064, DOI 10.1007/s006050050087
Bibliographic Information
- Frédéric Bayart
- Affiliation: USTL, Laboratoire AGAT, U.F.R. de Mathématiques, 59665 Villeneuve d’Ascq Cedex, France
- MR Author ID: 683115
- Email: bayart@agat.univ-lille1.fr
- Received by editor(s): October 9, 2001
- Received by editor(s) in revised form: January 16, 2002
- Published electronically: October 1, 2002
- Communicated by: N. Tomczak-Jaegermann
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1789-1791
- MSC (2000): Primary 47B38, 46B22
- DOI: https://doi.org/10.1090/S0002-9939-02-06759-X
- MathSciNet review: 1955266