| Remark on Regularity of Continuous Operators on AL-Spaces |
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| 作者姓名： | 冯勋省 陈滋利 |
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| 作者单位： | DepartmentofAppliedMathematics，SouthwestJiaotongUniversity，Chengdu610031,China |
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| 摘 要： | Let E and F be Banach lattices．It is known that if every continuous linear operator from E into F is regular，then，under some mild assumptions on E or F，either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space．Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice isregular．A counterex．ample is also provided，which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space．
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| 关 键 词： | 巴拿赫格子 原子数 整齐度 AL-空间 AM-空间 连续性操作 |
Remark on Regularity of Continuous Operators on AL-Spaces |
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| Feng Xunsheng,Chen Zili.Remark on Regularity of Continuous Operators on AL-Spaces[J].Journal of Southwest Jiaotong University,2004,12(1):79-82. |
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| Authors: | Feng Xunsheng Chen Zili |
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| Institution: | Department of Applied Mathematics, Southwest Jiaotong University, Chengdu 610031, China |
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| Abstract: | Let E and F be Banach lattices. It is known that if every continuous linear operator from E into F is regular, then, under some mild assumptions on E or F, either E is lattice isomorphic to an AL-space or F is lattice isomorphic to an AM-space. Here we present a characterization on an AL-space E such that every bounded linear operator from E into a Banach lattice is regular. A counterexample is also provided, which shows that the results are unexpected even if the domain is an AL-space or the range space is an AM-space. |
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| Keywords: | Banach lattice AL-space AM-space Atomicity Regularity |
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