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Proceedings of the American Mathematical Society

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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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  • Chandler Davis and Ciprian Foiaş, Operators with bounded characteristic function and their $J$-unitary dilation, Acta Sci. Math. (Szeged) 32 (1971), 127–139. MR 313845
  • 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
  • P. Ghatage, Power-bounded operators with invertible characteristic function, Acta Sci. Math. (Szeged) 37 (1975), no. 3-4, 201–204. MR 388144
  • 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, <IMG WIDTH="19" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$J$">-unitary dilation
Article copyright: © Copyright 1976 American Mathematical Society