Volterra算子与Toeplitz算子的乘积

Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (4): 829-836.

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The Product of Volterra Operator and Toeplitz Operator

Ding Xuanhao^1,²(),Shao Changhui¹(),Li Yongning^1,^2,^*()

¹School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
²Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067

Received:2023-05-25 Revised:2023-10-12 Online:2024-08-26 Published:2024-07-26
Supported by:
National Natural Science Foundation of China(12101092);Chongqing Natural Science Foundation(CSTB2022NSCQ-MSX1045);Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100822)

Abstract

Abstract:

In this paper, we study the product operators of Volterra operator $ V $ and Toeplitz operator $ T_\varphi $ on the classical Hardy space $ L_\varphi=T_\varphi V $ and $ R_\varphi=VT_\varphi $, and we obtain some basic properties of $ L_\varphi $ and $ R_\varphi $, we also get a result of $ L_\varphi $ which is similar to the Coburn theorem of Toeplitz operator. The necessary and sufficient conditions for $ V $ and $ T_\varphi $ to be commutative are given in this paper, and the symbol of $ L_\varphi $ and $ R_\varphi $ is characterized when $ z^jH^2\ (j=1, 2, \cdots ) $ are the common invariant subspaces of $ L_\varphi $ and $ R_\varphi $.

Key words: Volterra operator, Toeplitz operator, Coburn theorem, Commutative, Invariant subspace

CLC Number:

O177.1

Ding Xuanhao, Shao Changhui, Li Yongning. The Product of Volterra Operator and Toeplitz Operator[J].Acta mathematica scientia,Series A, 2024, 44(4): 829-836.

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The Product of Volterra Operator and Toeplitz Operator

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