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Strongly limited (Dunford–Pettis) completely continuous subspaces of operator ideals
Annals of Functional Analysis ( IF 1 ) Pub Date : 2019-12-04 , DOI: 10.1007/s43034-019-00039-8
Halimeh Ardakani , Manijeh Salimi , Seyed Mohammad Moshtaghioun

By introducing the concepts of strongly limited completely continuous and strongly Dunford–Pettis completely continuous subspaces of operator ideals, it will be given some characterizations of these concepts in terms of lcc ness and DPcc ness of all their evaluation operators related to that subspace. In particular, when $$X^*$$ or Y has the Gelfand–Phillips (GP) property, we give a characterization of GP property of a closed subspace $${\mathcal {M}}$$ of compact operators K(X, Y) in terms of strong limited complete continuity of $${\mathcal {M}}$$. Also it is shown that, each operator ideal $${\mathcal {U}}(X, Y )$$ is strongly limited completely continuous, iff, $$X^*$$ and Y have the GP property.

中文翻译:

算子理想的强有限(Dunford-Pettis)完全连续子空间

通过引入算子理想的强有限完全连续子空间和强Dunford-Pettis完全连续子空间的概念,将根据与该子空间相关的所有评估算子的lcc ness和DPcc ness给出这些概念的一些特征。特别地,当 $$X^*$$ 或 Y 具有 Gelfand–Phillips (GP) 性质时,我们给出了紧算子 K( X, Y) 在 $${\mathcal {M}}$$ 的强有限完全连续性方面。还表明,每个算子理想 $${\mathcal {U}}(X, Y )$$ 是强有限完全连续的,当当当,$$X^*$$ 和 Y 具有 GP 性质。
更新日期:2019-12-04
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