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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Double commutants of $ C\sb{\cdot 0}$ contractions. II


Author: Mitsuru Uchiyama
Journal: Proc. Amer. Math. Soc. 74 (1979), 271-277
MSC: Primary 47A45
DOI: https://doi.org/10.1090/S0002-9939-1979-0524299-5
MathSciNet review: 524299
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Abstract: In [13], it was shown that if T is a $ C{._0}$ contraction with finite defect indices $ \infty > {\delta _{{T^\ast}}} > {\delta _T}$, then $ \{ T\} '' = \{ \phi (T):\phi \in {H^\infty }\} $. In this note we shall extend this result to $ \infty \geqslant {\delta _{{T^\ast}}} > {\delta _T}$ and show that $ \{ T\} ''$ and $ {H^\infty }$ is isometric isomorphic, and moreover such an operator is reflexive.


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DOI: https://doi.org/10.1090/S0002-9939-1979-0524299-5
Keywords: $ {\text{C}}{._0}$ contraction, canonical functional model, double commutant, operator valued inner function, reflexive
Article copyright: © Copyright 1979 American Mathematical Society