群上的Toeplitz代数(英文)

Toeplitz Operator Algebras on Groups

研究了离散交换群上的Toeplitz算子和Toeplitz代数 .通过谱投影和Fourier变换 ,将离散交换群上的Toeplitz算子和Toeplitz代数的问题化成了其对偶群上的Hardy空间中的相应问题 ,并由此得到了Toeplitz算子的特征 (定理 10 ) ,约化Toeplitz代数与Toeplitz代数相等的充分必要性 (命题 5 )以及关于Toeplitz代数的短正合列(定理 6 )等一系列结果 .

In this paper we study Toeplitz operator and Toeplitz algebra on discrete abelian group. By the spectral projection and Fourier transformation, we transform the problem of Toeplitz operator and Toeplitz algebra on discrete ablien group into the problem of them on the Hardy space of the dual group. We conclude the character of Toeplitz operator(Theorem 10), the necessary and sufficient condition of that the reduced Toeplitz algebra equals Toeplitz algebra (Proposition 5)and the short exact sequence of Toeplitz algebra(Theorem 6).