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 ${H^\infty }$.References
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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