| 包含紧算子理想的Toeplitz算子代数的刻画 |
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| 引用本文： | 许庆祥. 包含紧算子理想的Toeplitz算子代数的刻画[J]. 数学进展, 2001, 30(5): 432-434 |
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| 作者姓名： | 许庆祥 |
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| 作者单位： | 上海师范大学数学科学学院, |
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| 基金项目： | Supported by the NSFC (No. 19901019) and the Youth Science Foundation of Shanghai Higher Education (No.98QN75). |
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| 摘 要： | 设G为一个torsion-free的离散群，（G，G＋）为一个拟序群，记T^G (G)为相应的Toeplitz算子代数，K(l^2(G 1)为l^2(G )上的紧算子全体，本文证明了K(l^2(G ))增包含于T^G (G)当且仅当下列两个条件时满足。（1）（G，G＋）为一个序群，（2）G中存在一个最小的正元。
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| 关 键 词： | 离散拟序群 Toeplitz算子 紧算子 torsion－free离散群 序群 最小正元 |
| 修稿时间： | 1999-03-30 |
A Character of Toeplitz Algebras Containing the Ideal of Compact Operators |
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| Xu Qingxiang. A Character of Toeplitz Algebras Containing the Ideal of Compact Operators[J]. Advances in Mathematics(China), 2001, 30(5): 432-434 |
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| Authors: | Xu Qingxiang |
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| Abstract: | Let G be a discrete torsion-free group and (G, G ) a quasi-ordered group. Let TG (G) be the corresponding Toeplitz algebra. In this note, we show that TG (G) contains the ideal of compact operators on 2(G ) if and only if the following two conditions are satisfied: (1) (G, G ) is an ordered group; (2) G admits a least positive element. |
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| Keywords: | discrete quasi-ordered group Toeplitz operator compact operator |
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