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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Double commutants of $C_{\cdot 0}$ contractions
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by Mitsuru Uchiyama PDF
Proc. Amer. Math. Soc. 69 (1978), 283-288 Request permission

Abstract:

D. Sarason has shown that an operator in the double commutant of a contraction T of class ${C_0}(1)$ is interpolated by a function in ${H^\infty }$, that is, $\{ T\} ’ = \{ \phi (T);\phi \in {H^\infty }\}$, [3]. Generally, in [4] Sz.-Nagy and C. Foiaş have shown that an operator in the double commutant of a contraction T of class ${C_0}(n)$ is interpolated by a function in ${N_T}$, that is, $\{ T\} '' = \{ {\phi _1}{(T)^{ - 1}}{\phi _2}(T):{\phi _2}/{\phi _1} \in {N_T}\}$. In this note we shall show that an operator in the double commutant of a ${C_{ \cdot 0}}$ contraction T with finite defect indices ${\delta _{{T^ \ast }}} > {\delta _T}$ is interpolated by a function in ${H^\infty }$.
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Additional Information
  • © Copyright 1978 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 69 (1978), 283-288
  • MSC: Primary 47A45
  • DOI: https://doi.org/10.1090/S0002-9939-1978-0482301-2
  • MathSciNet review: 0482301