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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] C. Davis and C. Foiaş, Operators with bounded characteristic function and their $ J$-unitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127-139. MR 47 #2398. MR 0313845 (47:2398)
  • [2] C. Foiaş, Some applications of structural models for operators on Hilbert space, Proc. Internat. Congress Math. (Nice, 1970), vol. 2, Gauthier-Villars, Paris, 1971, pp. 433-440. MR 0440390 (55:13265)
  • [3] P. Ghatage, Power bounded operators with invertible characteristic function, Acta Sci. Math. (Szeged) (to appear). MR 0388144 (52:8981)
  • [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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