Document Zbl 1423.47006

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Algebraic properties of Toeplitz operators with symbols from the range of the heat transform on the Fock space. (English) Zbl 1423.47006

Adv. Oper. Theory 4, No. 3, 698-723 (2019).

Summary: 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 results from the Bergman space to the Fock space setting.

MSC:

47B35	Toeplitz operators, Hankel operators, Wiener-Hopf operators
53D55	Deformation quantization, star products

Keywords:

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

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