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Extension of Positive Operators
Siberian Mathematical Journal ( IF 0.5 ) Pub Date : 2020-03-01 , DOI: 10.1134/s0037446620020081
K. Yu. Ilina , Z. A. Kusraeva

The main result states that if E is a separable Fréchet lattice and F is a (locally solid) topological vector lattice with the σ -interpolation property then each positive linear operator T 0 from a majorizing subspace G ⊂ E into F admits extension to a continuous positive linear operator T from E into F . This fact is proved by using only the axiom of countable choice.

中文翻译:

正运算符的扩展

主要结果表明,如果 E 是可分离的 Fréchet 格并且 F 是具有 σ 插值属性的(局部实心)拓扑向量格,那么从主化子空间 G ⊂ E 到 F 的每个正线性算子 T 0 允许扩展到连续从 E 到 F 的正线性算子 T 。这个事实只用可数选择公理来证明。
更新日期:2020-03-01
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