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Products of Toeplitz operators on the Fock space

Authors: Hong Rae Cho, Jong-Do Park and Kehe Zhu
Journal: Proc. Amer. Math. Soc. 142 (2014), 2483-2489
MSC (2010): Primary 47B35, 30H20
Published electronically: March 19, 2014
MathSciNet review: 3195769
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Abstract: 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

Jong-Do Park
Affiliation: School of Mathematics, KIAS, Hoegiro 87, Dongdaemun-gu, Seoul 130-722, Republic of Korea

Kehe Zhu
Affiliation: Department of Mathematics and Statistics, SUNY, Albany, New York 12222
MR Author ID: 187055

Keywords: Toeplitz operator, Fock space, Weierstrass factorization, Berezin transform
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.