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21.
In a vector lattice, ideals and bands are well-investigated subjects. We study similar notions in a pre-Riesz space. The pre-Riesz
spaces are exactly the order dense linear subspaces of vector lattices. Restriction and extension properties of ideals, solvex
ideals and bands are investigated. Since every Archimedean directed partially ordered vector space is pre-Riesz, we establish
properties of ideals and bands in such spaces.
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22.
Gregor Dolinar 《Proceedings of the American Mathematical Society》2002,130(1):129-138
Let and be compact Hausdorff spaces and let . A linear mapping is called -disjointness preserving if implies that . If is a continuous or surjective -disjointness preserving linear mapping, we prove that there exists a disjointness preserving linear mapping satisfying . We also prove that every unbounded -disjointness preserving linear functional on is disjointness preserving.
23.
张伟 《浙江大学学报(理学版)》1959,46(5):529-536
连续广义预框架算子是算子理论应用于连续广义框架理论的一类重要算子。利用连续广义预框架算子,刻画了连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基;利用算子工具,构造了新的连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基,并给出了相应的算子刻画;建立了连续广义预框架算子与强不相交性、不相交性以及强互补对之间的关系;最后,利用已建立的刻画结果,得到了两连续广义框架之和保持框架性质的算子刻画。 相似文献