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

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.