Advances in Operator Theory

Algebraic properties of Toeplitz operators with symbols from the range of the heat transform on the Fock space

Dieudonne Agbor

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Abstract

‎‎‎We develop new methods to study the zero product problem and the commutator of Toeplitz operators on the Fock space with harmonic symbols‎. ‎Our method gives us new results on the zero product problem and the commutator of Toeplitz operators on the Fock space‎. ‎We also extend some known result on the Bergman space setting to the Fock space‎.

Article information

Source
Adv. Oper. Theory, Volume 4, Number 3 (2019), 698-723.

Dates
Received: 7 September 2018
Accepted: 6 February 2019
First available in Project Euclid: 2 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.aot/1551495629

Digital Object Identifier
doi:10.15352/aot.1809-1416

Mathematical Reviews number (MathSciNet)
MR3919040

Zentralblatt MATH identifier
07056794

Subjects
Primary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]
Secondary: 53D55: Deformation quantization, star products

Keywords
Berezin transform‎ Fock space‎ ‎‎harmonic function ‎ ‎‎Toeplitz operator ‎ (semi-)commutator

Citation

Agbor, Dieudonne. Algebraic properties of Toeplitz operators with symbols from the range of the heat transform on the Fock space. Adv. Oper. Theory 4 (2019), no. 3, 698--723. doi:10.15352/aot.1809-1416. https://projecteuclid.org/euclid.aot/1551495629


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