Fock空间上径向函数诱导的Toeplitz算子

黄穗

数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 345-352.

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PDF(392 KB)
数学学报 ›› 2019, Vol. 62 ›› Issue (2) : 345-352. DOI: 10.12386/A2019sxxb0032
论文

Fock空间上径向函数诱导的Toeplitz算子

    黄穗
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Toeplitz Operators with Radial Symbols on Fock Space

    Sui HUANG
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文章历史 +

摘要

本文讨论了 Fock空间上以径向函数和拟齐次函数为符号的 Toeplitz算子的代数性质,给出了两个以径向函数为符号的 Toeplitz 算子的积仍为Toeplitz 算子的充分必要条件, 并且研究了以拟齐次函数为符号的Toeplitz 算子的交换性.

Abstract

We discuss some algebraic properties of Toeplitz operators with a class of radial and quasi-homogeneous symbols on the Fock space of the complex plane. We give necessary and sufficient conditions for the product of two Toeplitz operators with radial symbols to be a Toeplitz operator, and study the zero-product problem of several such Toeplitz operators. Furthermore, the corresponding commuting problem of Toeplitz operators with quasi-homogeneous symbols is studied.

关键词

Toeplitz 算子 / Fock 空间 / 径向函数 / 拟齐次函数

Key words

Toeplitz operator / Fock space / radial function / quasi-homogeneous function

引用本文

导出引用
黄穗. Fock空间上径向函数诱导的Toeplitz算子. 数学学报, 2019, 62(2): 345-352 https://doi.org/10.12386/A2019sxxb0032
Sui HUANG. Toeplitz Operators with Radial Symbols on Fock Space. Acta Mathematica Sinica, Chinese Series, 2019, 62(2): 345-352 https://doi.org/10.12386/A2019sxxb0032

参考文献

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基金

国家自然科学基金资助项目(11501068);重庆市教委科研资助项目(KJ1600302)

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