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Proceedings of the American Mathematical Society

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

 

 

A structure theorem for the commutant of a class of cyclic subnormal operators


Author: Marc Raphael
Journal: Proc. Amer. Math. Soc. 96 (1986), 318-322
MSC: Primary 47B20; Secondary 47B38
DOI: https://doi.org/10.1090/S0002-9939-1986-0818465-2
MathSciNet review: 818465
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Abstract: An $ m$-measure is defined to be a measure $ \mu $ such that the analytic bounded point evaluations of $ {P^2}(\mu )$ is the open unit disk $ {\mathbf{D}}$ in the complex plane, and the weak* closure of the analytic polynomials in $ {L^\infty }(\mu )$ is the set of bounded analytic functions on $ {\mathbf{D}}$. A complete characterization of $ {P^2}(\mu ) \cap {L^\infty }(\mu )$, the commutant of the cyclic subnormal operator of multiplication by $ z$ on $ {P^2}(\mu )$, is then obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818465-2
Article copyright: © Copyright 1986 American Mathematical Society