Products of Toeplitz operators on the Fock space
HTML articles powered by AMS MathViewer
- by Hong Rae Cho, Jong-Do Park and Kehe Zhu PDF
- Proc. Amer. Math. Soc. 142 (2014), 2483-2489 Request permission
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.References
- H. R. Cho, B. R. Choe and H. Koo, Linear combinations of composition operators on the Fock-Sobolev spaces, preprint.
- Hong Rae Cho and Kehe Zhu, Fock-Sobolev spaces and their Carleson measures, J. Funct. Anal. 263 (2012), no. 8, 2483–2506. MR 2964691, DOI 10.1016/j.jfa.2012.08.003
- Svante Janson, Jaak Peetre, and Richard Rochberg, Hankel forms and the Fock space, Rev. Mat. Iberoamericana 3 (1987), no. 1, 61–138. MR 1008445, DOI 10.4171/RMI/46
- Jong-Do Park, Bounded Toeplitz products on the Bergman space of the unit ball in ${\Bbb C}^n$, Integral Equations Operator Theory 54 (2006), no. 4, 571–584. MR 2222985, DOI 10.1007/s00020-005-1405-1
- V. P. Havin and N. K. Nikolski (eds.), Linear and complex analysis. Problem book 3. Part I, Lecture Notes in Mathematics, vol. 1573, Springer-Verlag, Berlin, 1994. MR 1334345
- Karel Stroethoff and Dechao Zheng, Products of Hankel and Toeplitz operators on the Bergman space, J. Funct. Anal. 169 (1999), no. 1, 289–313. MR 1726756, DOI 10.1006/jfan.1999.3489
- Karel Stroethoff and Dechao Zheng, Bounded Toeplitz products on the Bergman space of the polydisk, J. Math. Anal. Appl. 278 (2003), no. 1, 125–135. MR 1963469, DOI 10.1016/S0022-247X(02)00578-4
- Karel Stroethoff and Dechao Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007), no. 1, 114–129. MR 2273032, DOI 10.1016/j.jmaa.2006.01.009
- Dechao Zheng, The distribution function inequality and products of Toeplitz operators and Hankel operators, J. Funct. Anal. 138 (1996), no. 2, 477–501. MR 1395967, DOI 10.1006/jfan.1996.0073
- Kehe Zhu, Analysis on Fock spaces, Graduate Texts in Mathematics, vol. 263, Springer, New York, 2012. MR 2934601, DOI 10.1007/978-1-4419-8801-0
Additional Information
- Hong Rae Cho
- Affiliation: Department of Mathematics, Pusan National University, Pusan 609-735, Republic of Korea
- Email: chohr@pusan.ac.kr
- Jong-Do Park
- Affiliation: School of Mathematics, KIAS, Hoegiro 87, Dongdaemun-gu, Seoul 130-722, Republic of Korea
- Email: jdpark@kias.re.kr
- Kehe Zhu
- Affiliation: Department of Mathematics and Statistics, SUNY, Albany, New York 12222
- MR Author ID: 187055
- Email: kzhu@math.albany.edu
- 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: https://doi.org/10.1090/S0002-9939-2014-12110-1
- MathSciNet review: 3195769