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Proceedings of the American Mathematical Society

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

 

 

On the reflexivity of $ C\sb{0}(N)$ contractions


Author: Pei Yuan Wu
Journal: Proc. Amer. Math. Soc. 79 (1980), 405-409
MSC: Primary 47A45
DOI: https://doi.org/10.1090/S0002-9939-1980-0567981-4
MathSciNet review: 567981
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Abstract: Let T be a $ {C_0}(N)$ contraction on a separable Hilbert space and let $ J = S({\varphi _1}) \oplus S({\varphi _2}) \oplus \cdots \oplus S({\varphi _k})$ be its Jordan model, where $ {\varphi _1},{\varphi _2}, \ldots ,{\varphi _k}$ are inner functions satisfying $ {\varphi _j}\vert{\varphi _{j - 1}}$ for $ j = 2,3, \ldots ,k$, and $ S({\varphi _j})$ denotes the compression of the shift on $ {H^2} \ominus {\varphi _j}{H^2},j = 1,2, \ldots ,k$. In this note we show that T is reflexive if and only if $ S({\varphi _1}/{\varphi _2})$ is.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0567981-4
Keywords: $ {C_0}(N)$, reflexive operator, Jordan model for $ {C_0}(N)$ contractions, quasi-similarity
Article copyright: © Copyright 1980 American Mathematical Society