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Characteristic functions of operators similar to unitary operators

Author: P. Ghatage
Journal: Proc. Amer. Math. Soc. 59 (1976), 62-64
MSC: Primary 47A45
MathSciNet review: 0420308
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Abstract: Suppose $ T$ denotes an operator which is similar to a unitary operator and $ {\theta _T}$ denotes its characteristic function--considered as an operator on $ {H^2}({D_T})$. It is proved that $ {\theta _T}$ is a bounded operator if and only if it is the inverse of a bounded operator.

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  • [1] Chandler Davis and Ciprian Foiaş, Operators with bounded characteristic function and their 𝐽-unitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127–139. MR 0313845
  • [2] Ciprian Foiaş, Some applications of structural models for operators on Hilbert space, Actes du Congrès International des Mathématiciens (Nice, 1970) Gauthier-Villars, Paris, 1971, pp. 433–440. MR 0440390
  • [3] P. Ghatage, Power-bounded operators with invertible characteristic function, Acta Sci. Math. (Szeged) 37 (1975), no. 3-4, 201–204. MR 0388144
  • [4] B. Sz.-Nagy and C. Foiaş, Analyse harmonique des opérateurs de l'espace de Hilbert, Masson, Paris; Akad. Kiadó, Budapest, 1967; English Rev. transl., North-Holland, Amsterdam; American Elsevier, New York; Akad. Kiadó, Budapest, 1970. MR 37 #778; 43 #947.

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Keywords: Characteristic function, $ J$-unitary dilation
Article copyright: © Copyright 1976 American Mathematical Society

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