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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles 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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Products of Toeplitz operators on the Fock space
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by Hong Rae Cho, Jong-Do Park and Kehe Zhu PDF
Proc. Amer. Math. Soc. 142 (2014), 2483-2489 Request permission


Let $f$ and $g$ be functions, not identically zero, in the Fock space $F^2_\alpha$ of $\mathbb {C}^n$. We show that the product $T_fT_{\overline g}$ of Toeplitz operators on $F^2_\alpha$ is bounded if and only if $f(z)=e^{q(z)}$ and $g(z)=ce^{-q(z)}$, where $c$ is a nonzero constant and $q$ is a linear polynomial.
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Additional Information
  • Hong Rae Cho
  • Affiliation: Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea
  • Email:
  • Jong-Do Park
  • Affiliation: School of Mathematics, KIAS, Hoegiro 87, Dongdaemun-gu, Seoul 130-722, Republic of Korea
  • Email:
  • Kehe Zhu
  • Affiliation: Department of Mathematics and Statistics, SUNY, Albany, New York 12222
  • MR Author ID: 187055
  • Email:
  • Received by editor(s): August 3, 2012
  • Published electronically: March 19, 2014
  • Additional Notes: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2011-0013740 for the first author) and (NRF-2010-0011841 for the second author)
  • Communicated by: Richard Rochberg
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2483-2489
  • MSC (2010): Primary 47B35, 30H20
  • DOI:
  • MathSciNet review: 3195769