Hyponormality of Toeplitz operators on the Fock spaces

ABSTRACT

In this paper, we consider the hyponormality of Toeplitz operators $T_{\varphi }$ on the Fock spaces ${\mathbb{F}}^2$. First we characterize the necessary and sufficient conditions for the hyponormality of Toeplitz operators $T_{\varphi }$ on ${\mathbb{F}}^2$ with some symbol ϕ in the class of functions $f+\overline{g}$ with polynomials f and g. Next, we consider the necessary condition for hyponormality of $T_{\varphi }$ with trigonometric polynomial symbol ϕ.

KEYWORDS:

• Toeplitz operators
• hyponormal
• Fock space

AMS SUBJECT CLASSIFICATIONS:

• 47A62
• 47B15
• 47B20

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2016R1D1A1B03931937). The second author was supported by Brain Korea 21 plus Mathematical Science Team for Global Women Leaders at Ewha Womans University and the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2018R1D1A1B07048620).