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Similarity to an isometry of a composition operator

Author(s): Frédéric Bayart
Journal: Proc. Amer. Math. Soc. 131 (2003), 1789-1791.
MSC (2000): Primary 47B38, 46B22
Posted: 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:

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F. Bayart, De nouveaux espaces de séries de Dirichlet et leurs opérateurs de composition, CRAS 333 (2001), 207-212 MR 2002f:47051

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C.C Cowen and B.D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton (1995) MR 97i:47056

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J.Cima, J.Thomson, W. Wogen, On some properties of Composition Operators, Ind. Math. Journal 24 (1974), 215-221 MR 50:2979

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N.Jaoua, Similarity to a contraction and hypercontractivity of composition operators, Proceedings of the American Math. Society 129 (2001), 2085-2092 MR 2002d:47038

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E.Nordgren, Composition operators, Can. J. Math. 20 (1968), 442-449 MR 36:6961

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J.H. Shapiro, What do composition operators know about inner functions?, Monat Math 130 (2000), 57-70 MR 2001a:47029

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Additional Information:

Frédéric Bayart
Affiliation: USTL, Laboratoire AGAT, U.F.R. de Mathématiques, 59665 Villeneuve d'Ascq Cedex, France
Email: bayart@agat.univ-lille1.fr

DOI: 10.1090/S0002-9939-02-06759-X
PII: S 0002-9939(02)06759-X
Keywords: Similarity to an isometry, composition operator, Hardy space
Received by editor(s): October 9, 2001
Received by editor(s) in revised form: January 16, 2002
Posted: October 1, 2002
Communicated by: N. Tomczak-Jaegermann
Copyright of article: Copyright 2002, American Mathematical Society

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