| 套的间断点与套代数的理想 |
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| 引用本文： | 陈培鑫,柳景霜,杨洪格. 套的间断点与套代数的理想[J]. 南京理工大学学报(自然科学版), 2009, 33(5) |
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| 作者姓名： | 陈培鑫 柳景霜 杨洪格 |
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| 作者单位： | 1. 南京理工大学,理学院,江苏,南京,210094
2. 包头师范学院,数学科学学院,内蒙古,包头,014010 |
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| 基金项目： | 国家自然科学基金(10771101) |
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| 摘 要： | 设N是一个赋范线性空间X上的套,m(N)是N到N的映射全体所成的集合,记m0(N)={α∈m(N)|α(0)=0,α左连续且保序}。对于子空间M,首先表明下面命题是等价的:(1)M是弱闭的AlgN-模;(2)存在α∈m0(N)使M=Mα;(3)存在β∈m(N)使M=Mβ。假使N最多只包含3个元素,那么所有的AlgN-模可全部被列举出来;假如N至少包含4个元素,那么下面命题是等价的:(1)0<0+且X-
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| 关 键 词： | 套 套代数 2-阶间断点 外模 极大（小）理想 |
Discontinuous Points of Nests and Some Ideals of Nest Algebras |
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| CHEN Pei-xin,LIU Jing-shuang,YANG Hong-ge. Discontinuous Points of Nests and Some Ideals of Nest Algebras[J]. Journal of Nanjing University of Science and Technology(Nature Science), 2009, 33(5) |
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| Authors: | CHEN Pei-xin LIU Jing-shuang YANG Hong-ge |
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| Affiliation: | 1.School of Sciences;NUST;Nanjing 210094;China;2.Mathematical Science College;Baotou Teachers' College;Baotou 014010;China |
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| Abstract: | Let N be a nest on a fixed linear norm space X, m(N) be the set of all maps of N into itself, put m_0(N)={α∈m(N)α(0)=0, α is order preserving and left continuous}. For a subspace M, we first show that the following three statements are equivalent: (1)M is a weakly closed AlgN-module; (2)there exists α∈m_0(N) such that M=M_α; (3)there exists β∈m(N) such that M=M_β. If N contains 3 elements at most, the all weakly closed AlgN-modules can be listed; if N contains 4 elements at least, then the following statements are equivalent: (1)0<0~+and X~-
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| Keywords: | nests nest algebra two-order discintinuous points outer modules maximal (minimal) ideals |
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