| CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES |
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| 引用本文： | Han Deguang. CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONS OF NEST ALGEBRAS ON BANACH SPACES[J]. 数学年刊B辑(英文版), 1996, 17(2): 227-236 |
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| 作者姓名： | Han Deguang |
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| 作者单位： | HAN DEGUANG Department of Mathematics，Qufa Normal University，Qufu 273165，Shandong，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of Chin |
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| 摘 要： | This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional.
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| 关 键 词： | 嵌套代数 巴拿赫空间 连续性 线性 |
| 收稿时间： | 1993-07-05 |
| 修稿时间： | 1994-07-02 |
CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONSOF NEST ALGEBRAS ON BANACH SPACES |
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| Han Deguang. CONTINUITY AND LINEARITY OF ADDITIVE DERIVATIONSOF NEST ALGEBRAS ON BANACH SPACES[J]. Chinese Annals of Mathematics,Series B, 1996, 17(2): 227-236 |
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| Authors: | Han Deguang |
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| Affiliation: | DepartmentofMathematics,QufaNormalUniversity,Qufu273165,Shandong,China. |
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| Abstract: | This paper discusses the problem concerning the continuity and linearity of additive derivation of nest algebras on normed spaces. It is proved that every linear derivation of a nest algebraalgN is continuous provided that one of the following conditions is satisfied: (1) 0 (?) 0. (2)X_ (?) X. (3) there exists a non-trivial idempotent p in algN such that the range of p belongsto N. It is also proved that every additive derivation of a nest algebra is automatically linearif the underlying normed space is infinite dimemnsional. |
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| Keywords: | Nest algebra Derivation Continuity Linearity Banach space |
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