| 向量测度的算子分解 |
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| 引用本文： | 黄雪冰,施慧华.向量测度的算子分解[J].华侨大学学报(自然科学版),2014,0(2):238-240. |
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| 作者姓名： | 黄雪冰 施慧华 |
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| 作者单位： | 华侨大学 数学科学学院, 福建 泉州 362021 |
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| 基金项目： | 国家自然科学基金专项数学天元基金资助项目(11226129);华侨大学高层次人才科研启动项目(10BS215) |
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| 摘 要： | 利用向量测度与算子的一一对应关系,给出可列可加测度的算子表示,并进一步由推广的Yosida-Hewitt定理证明定义在B(Ω,Σ)=span^-{χA,A∈Σ}上的取值于自反空间X的算子,可唯一分解成w*-范序列连续算子与纯连续算子之和.
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| 关 键 词： | *-范序列w*-范序列 连续算子 纯连续算子 向量测度 Yosida-Hewitt定理 |
Operator Decomposition of Vector Measures |
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| HUANG Xue-bing;SHI Hui-hua.Operator Decomposition of Vector Measures[J].Journal of Huaqiao University(Natural Science),2014,0(2):238-240. |
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| Authors: | HUANG Xue-bing;SHI Hui-hua |
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| Institution: | School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China |
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| Abstract: | Using the isometrim between vector measures and operators, we give the operator representation for countably additive measures, then by applying extended Yosida-Hewitt theorem we show that a operator, which defined on B(Ω,Σ)=span^-{χA,A∈Σ} and valued in the reflexive Banach space, X can be uniquely decomposed into the sum of a w*-norm sequentially continuous operator and a purely continuous operator. |
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| Keywords: | *-norm sequentially continuousw*-norm sequentially continuous continuous operator purely continuous operator vector measures Yosida-Hewitt theorem |
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