Journal of Operator Theory

Volume 84, Issue 1, Summer 2020 pp. 35-47.

Mixed products of Toeplitz and Hankel operators on the Fock space

Authors: Pan Ma

$1$ , Fugang Yan

$2$ , Dechao Zheng

$3$ , Kehe Zhu,

$4$
Author institution:

$1$ School of Mathematics and Statistics, Central South University, Hunan 410083, China

$2$ College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China, and Department of Mathematics and Statistics, SUNY, Albany, NY 12222, U.S.A.

$3$ Department of Mathematics, Vanderbilt University, Nashville, TN 37240, U.S.A. and Center of Mathematics, Chongqing University, Chongqing 401331, China

$4$ Department of Mathematics and Statistics, SUNY, Albany, NY 12222, U.S.A. and Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China

Summary: For entire functions

$f$ and

$g$ we determine exactly when the product

$H_{\overline f}T_{\overline g}$ of the Hankel operator

$H_{\overline f}$ and the Toeplitz operator

$T_{\overline g}$ is bounded on the Fock space

$F^2_\alpha$ . This solves a natural companion to Sarason's Toeplitz product problem.

DOI: http://dx.doi.org/10.7900/jot.2018dec10.2246
Keywords: Toeplitz operators, Hankel operators, Fock space, Berezin transform

Contents Full-Text PDF