| 超有限Ⅱ_1型因子中Cartan双模代数上等距和2-局部等距 |
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| 引用本文： | 纪培胜,魏翠萍. 超有限Ⅱ_1型因子中Cartan双模代数上等距和2-局部等距[J]. 数学学报, 2006, 49(1): 51-58. DOI: cnki:ISSN:0583-1431.0.2006-01-010 |
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| 作者姓名： | 纪培胜 魏翠萍 |
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| 作者单位： | [1]青岛大学数学系,青岛266071 [2]曲阜师范大学（日照校区）运筹与管理学院,日照276826 |
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| 基金项目： | 国家自然科学基金资助项目（10371061）;数学天元基金资助项目（A0324614） |
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| 摘 要： | 设M是超有限Ⅱ1型因子．D是M的Cartan子代数,T是对角为D的M 的σ-弱闭的子代数(简称Cartan双模代数)并且生成M．设φ是T到T上的σ-弱连续满线性等距,则Φ可扩张成从M到M上的等距．设φ是T到T上的映射(没假设线性),满足任给a,b∈T,T上存在σ-弱连续满线性等距φa,b(与n,b有关),使得φa,b(a)=φ(a),φa,b(b)=φ(b),则φ是线性等距．
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| 关 键 词： | 超有限Ⅱ1型因子 σ-弱连续满线性等距 2-局部σ-弱连续满线性等距 |
| 文章编号： | 0583-1431（2006）01-0051-08 |
| 收稿时间： | 2004-06-01 |
| 修稿时间： | 2004-06-012004-10-25 |
Isometries and 2-Local Isometries on Cartan Bimodule Algebras in Hyperfinite Factors of Type Ⅱ_1 |
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| Pei Sheng JI,Cui Ping WEI. Isometries and 2-Local Isometries on Cartan Bimodule Algebras in Hyperfinite Factors of Type Ⅱ_1[J]. Acta Mathematica Sinica, 2006, 49(1): 51-58. DOI: cnki:ISSN:0583-1431.0.2006-01-010 |
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| Authors: | Pei Sheng JI Cui Ping WEI |
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| Affiliation: | Pei Sheng JI Department of Mathematics, Qingdao University, Qingdao 266071, P. R. China Cui Ping WEI Institute of Operations Research, Qufu Normal University, Rizhao 276826, P. R. China |
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| Abstract: | Let M be a hyperfinite factor of type Ⅱ1, D is a Cartan masa of M, T be a Cartan subalgebas of M with diagonal D which generates M. If Φ: T →T be an σ-weakly continuous (Banach) isometry, then Φ can be extended a isometry on M.If a map Φ: T→T satisfies that for every pair a, b ∈ T, there is a oooooooooo-weakly continuous isometry Φa,b on T such that Φa,b(a) = Φ(a), Φ>a,b(b) = Φ(b), then Φ is a linear isometry. |
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| Keywords: | hyperfinite factor of type Ⅱ1 σ-weakly continuous isometry 2-local σ-weakly continuous isometry |
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