| 沈钦锐.Banach空间中不等价算子非紧性测度[J].,2019,59(2):211-217 |
| Banach空间中不等价算子非紧性测度 |
| Inequivalent measure of noncompactness of operators in Banach spaces |
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| DOI：10.7511/dllgxb201902014 |
| 中文关键词:非紧性测度算子非紧性测度不等价测度Banach空间 |
| 英文关键词:measure of noncompactnessmeasure of noncompactness of operatorsinequivalent measureBanach space |
| 基金项目:国家自然科学基金青年基金资助项目(11801255)；高校博士科研启动基金资助项目(L21704)；福建省中青年教师教育科研项目(JAT170337). |
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| 中文摘要: |
| 用新的观点研究Banach空间中的算子非紧性测度．Banach空间X上的非空有界闭凸集构成的集族C(X)在通常的集合加法和数乘运算下可赋予范数构成赋范半群；接着利用序等距映射、格理想和抽象M空间等理论，在Banach空间上给出一个齐次算子非紧性测度的构造定理，并利用此定理证明了具有无限分解的Banach空间，特别地，具有无条件基的Banach空间上都存在着与Hausdorff非紧性测度不等价的齐次算子非紧性测度． |
| 英文摘要: |
| A new point of view is used to study the measure of noncompactness of operators in Banach space. The family C(X) of nonempty bounded closed convex sets on Banach space X can assign norms to form normed semigroups under normal set addition and multiplication operations. Then the theories of ordered equidistant mapping, lattice ideal and abstract M-space are used to give a construction theorem of measure of noncompactness of homogeneous operators in Banach space. Finally this theorem is used to prove that every Banach space with infinite decomposition, in particular, admitting an unconditional basis has a measure of noncompactness of homogeneous operators which is not equivalent to the Hausdorff measure of noncompactness of operators. |
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