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Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space

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  • Dieudonne Agbor

Abstract

We study some algebraic properties of Toeplitz operators with radial and quasi homogeneous symbols on the pluriharmonic Fock space over $\mathbb{C}^{n}$. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator, the zero-product problem for the product of two Toeplitz operators. Next we characterize the commutativity of Toeplitz operators with quasi homogeneous symbols and finally we study finite rank of the product of Toeplitz operators with quasi homogeneous symbols.

Suggested Citation

  • Dieudonne Agbor, 2017. "Algebraic Properties of Toeplitz Operators on the Pluri-harmonic Fock Space," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(6), pages 67-81, December.
    • Handle: RePEc:ibn:jmrjnl:v:9:y:2017:i:6:p:67
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    More about this item

    Keywords

    Fock space; Mellin transform; Pluriharmonic Fock space; Toeplitz operators.;
    All these keywords.

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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