| 套代数的直和分解 |
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| 引用本文： | 杜鸿科,杨有龙. 套代数的直和分解[J]. 数学学报, 1995, 38(6): 782-788. DOI: cnki:ISSN:05831431.0.1995-06-008 |
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| 作者姓名： | 杜鸿科 杨有龙 |
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| 作者单位： | 陕西师范大学数学系 |
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| 摘 要： | 本文主要研究套代数的直和分解。刻划了满足条件的交换子空间格Ｌ的结构，其中Ｒ是套代数的某一特殊子空间；得到了套代数分解成对角代数与某些特殊理想（例如：Ｊａｃｏｂｓｏｎ根或者Ｌａｒｓｏｎ理想）的直和的充要条件，同时也刻划了的一个范数闭左理想上Ｊ＿Ｎ最后，研究了对角代数与某些超因果理想直和的结构。
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| 关 键 词： | 套代数，Larson理想，期望，导子，交换子空间格 |
| 收稿时间： | 1993-07-02 |
| 修稿时间： | 1994-01-12 |
Decomposition of Nest Algebras in Direct Sums |
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| DuHongke,YongYoulong. Decomposition of Nest Algebras in Direct Sums[J]. Acta Mathematica Sinica, 1995, 38(6): 782-788. DOI: cnki:ISSN:05831431.0.1995-06-008 |
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| Authors: | DuHongke YongYoulong |
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| Affiliation: | DuHongke;YongYoulong(Department of Mathematics,Shanxi Normal University,Xi’n 710062,China) |
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| Abstract: | In this paper the main goal is to discuss decompositions of nest algebras T(N)in direct sums. Firstly we give a characterization of the commutative subspace lattice L which is with T(N)=R alg L,where R is a special subspace of nest algebra T(N),and obtain the sufficient and necessary condition of T(N)to be decomposed into the direct sum of its diagonal and its ideals(i.e.,Jacobson radical and Larson ideal),at the same time,we characterize a closedleft ideal J_N of T(N).Finally we study the direct sums of the diagonal of T(N)and some of itshypercausal ideals. |
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| Keywords: | nest algebra Larson’s ideal expectation derivation commutative subspace lattice |
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