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Proceedings of the American Mathematical Society

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

 
 

 

Subnormal composition operators


Author: Alan Lambert
Journal: Proc. Amer. Math. Soc. 103 (1988), 750-754
MSC: Primary 47B20; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
MathSciNet review: 947651
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Abstract: Let $ C$ be the composition operator on $ {L^2}(X,\Sigma ,m)$ given by $ Cf = f \circ T$, where $ T$ is a $ \Sigma $-measurable transformation from $ X$ onto $ X$ and $ {T^{ - 1}}/dm$ is strictly positive and bounded. It is shown that $ C$ is a subnormal operator if and only if the sequence $ dm \circ {T^{ - n}}/dm$ is a moment sequence for almost every point in $ X$. Several examples of subnormal composition operators are included.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0947651-8
Article copyright: © Copyright 1988 American Mathematical Society

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