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.
"Algebraic properties of Toeplitz operators with symbols from the range of the heat transform on the Fock space." Adv. Oper. Theory 4 (3) 698 - 723, Summer 2019. https://doi.org/10.15352/aot.1809-1416