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Criteria for Toeplitz operators on the sphere


Author: Jingbo Xia
Journal: Proc. Amer. Math. Soc. 141 (2013), 637-644
MSC (2010): Primary 46L10, 47B35
DOI: https://doi.org/10.1090/S0002-9939-2012-11489-3
Published electronically: July 2, 2012
MathSciNet review: 2996968
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Abstract: Let $ H^{2}(S)$ be the Hardy space on the unit sphere $ S$ in $ {\text {\bf C}}^{n}$. We show that a set of inner functions $ \Lambda $ is sufficient for the purpose of determining which $ A\in {\mathcal {B}}(H^{2}(S))$ is a Toeplitz operator if and only if the multiplication operators $ \{M_{u} : u \in \Lambda \}$ on $ L^{2}(S,d\sigma )$ generate the von Neumann algebra $ \{M_{f} : f \in L^{\infty }(S,d\sigma )\}$.


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Additional Information

Jingbo Xia
Affiliation: Department of Mathematics, State University of New York at Buffalo, Buffalo, New York 14260
Email: jxia@acsu.buffalo.edu

DOI: https://doi.org/10.1090/S0002-9939-2012-11489-3
Received by editor(s): December 18, 2010
Received by editor(s) in revised form: July 10, 2011
Published electronically: July 2, 2012
Communicated by: Marius Junge
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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