郭训香.离散交换群上Toeplitz 算子的代数性质[J].数学研究及应用,2008,28(2):396~402
离散交换群上Toeplitz 算子的代数性质
Algebraic Properties of Toeplitz Operators on Discrete Commutative Groups
投稿时间:2006-03-15  修订日期:2007-08-28
DOI:10.3770/j.issn:1000-341X.2008.02.021
中文关键词:  离散交换群  几乎不变集  Toeplitz 算子  亚正规算子  Hankle算子  解析Toeplitz算子.
英文关键词:discrete commutative group  almost stable subset  Toeplitz operator  hyponormal operator  Hankle operator  analytic Toeplitz operator.
基金项目:江西省自然科学基金(No.2007GZS0371).
作者单位
郭训香 赣南师范学院数学与计算机学院, 江西 赣州 341000 
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中文摘要:
      广泛的意义下定义 Toeplitz 算子, 给出了Toeplitz 算子乘积仍为Toeplitz 算子的充分必要条件, Toeplitz算子是正规算子的充分必要条件以及 Toeplitz 算子可交换的一个必要条件,从而推广了经典 Toeplitz 算子的相应结果.
英文摘要:
      In this paper, a generalized Toeplitz operator is defined and some of results about the classical Toeplitz operator are generalized. In particular, we obtain the necessary and sufficient condition for the product of two such Toeplitz operators to still be Toeplitz operator and the necessary and sufficient condition for such Toeplitz operator to be normal operator. Finally, a necessary condition for two such Toeplitz operators to be commutative is established.
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