Volterra算子与Toeplitz算子的乘积  

The Product of Volterra Operator and Toeplitz Operator

作　　者：丁宣浩[1,2] 邵长慧 李永宁 Ding Xuanhao;Shao Changhui;Li Yongning(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067;Chongqing Key Laboratory of Social Economy and Applied Statistics,Chongqing 400067)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067 [2]经济社会应用统计重庆市重点实验室,重庆400067

出　　处：《数学物理学报（A辑）》2024年第4期829-836,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(12101092);重庆市自然科学基金(CSTB2022NSCQ-MSX1045);重庆市教委科学技术研究项目(KJQN202100822)。

摘　　要：该文研究了经典Hardy空间上的Volterra算子V与Toeplitz算子T_(φ)的乘积算子L_(φ)=T_(φ)V与R_(φ)=VT_(φ),得到了L_(φ)与R_(φ)的一些基本性质,并给出了L_(φ)的类似于Toeplitz算子的Coburn定理的结果.该文还给出了V和T_(φ)可交换的充分必要条件,以及L_(φ)及R_(φ)以ZjH2(j=1,2,…)为不变子空间的符号的充要刻画.In this paper,we study the product operators of Volterra operator V and Toeplitz operator T_(φ)on the classical Hardy space L_(φ)=T_(φ)V and R_(φ)=VT_(φ),and we obtain some basic properties of L_(φ)and R_(φ),we also get a result of L_(φ)which is similar to the Coburn theorem of Toeplitz operator.The necessary and sufficient conditions for V and T_(φ)to be commutative are given in this paper,and the symbol of L_(φ)and R_(φ)is characterized when zjH2(j=1,2,⋯)are the common invariant subspaces of L_(φ)and R_(φ).

关 键 词：VOLTERRA算子 TOEPLITZ算子 Coburn定理 可交换 不变子空间 

分 类 号：O177.1[理学—数学]