Hyponormality of Toeplitz operators in several variables by the weighted shifts approach

ABSTRACT

In this paper, we characterize hyponormality of a class of operators related to a tuple of weighted shifts. As applications we construct examples of hyponormal Toeplitz operators on Hilbert spaces of holomorphic functions on the polydisk or the unit ball which include the Bergman space of the polydisk, the Hardy space of the unit ball and the Drury-Arveson space.

KEYWORDS:

• Hyponormal Toeplitz operators
• weighted shifts
• weighted Hardy space
• weighted Bergman space
• Drury-Arveson space

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 47A13
• 47B20
• 47B35

Acknowledgments

The work of the second and the third authors was undertaken during winter and/or summer breaks of 2016 and 2017 at California Polytechnic State University. They would like to take this opportunity to thank the Department of Mathematics, California Polytechnic State University, for the hospitality they received during their stay.

Disclosure statement

No potential conflict of interest was reported by the authors.

The work of the second author was supported by NRF(Korea) grant No. 2016R1A2B4012378. The work of the third author was supported by NRF(Korea) grant No. 2015R1D1A1A01058036.

Additional information

Funding

The work of the second author was supported by National Research Foundation (Korea) grant No. 2016R1A2B4012378. The work of the third author was supported by National Research Foundation (Korea) grant No. 2015R1D1A1A01058036.