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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Criteria for Toeplitz operators on the sphere
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by Jingbo Xia PDF
Proc. Amer. Math. Soc. 141 (2013), 637-644 Request permission

Abstract:

Let $H^{2}(S)$ be the Hardy space on the unit sphere $S$ in $\mathbf {C}^{n}$. 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
  • MR Author ID: 215486
  • Email: jxia@acsu.buffalo.edu
  • 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
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2996968