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Proceedings of the American Mathematical Society

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

 

 

Cyclic vectors in $ A^{-\infty}$


Authors: Leon Brown and Boris Korenblum
Journal: Proc. Amer. Math. Soc. 102 (1988), 137-138
MSC: Primary 46E10,; Secondary 30H05,46J15,47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0915731-9
MathSciNet review: 915731
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Abstract: If $ f$ is in $ {A^{ - p}}$, then $ f$ is cyclic in $ {A^{ - \infty }}$ if and only if $ f$ is cyclic in every $ {A^{ - q}}(q{\text{ > }}p)$. An analogous result holds for the Bergman spaces $ {B^p}$.

In this note we apply the theory developed in [2 and 3] to explain the relationship between cyclic vectors in $ {A^{ - \infty }}$ and $ {A^{ - p}}$ or $ {B^p}$.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0915731-9
Article copyright: © Copyright 1988 American Mathematical Society