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An Asplund space with norming Markuševič basis that is not weakly compactly generated
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-09-20 , DOI: 10.1016/j.aim.2021.108041 Petr Hájek 1 , Tommaso Russo 1, 2 , Jacopo Somaglia 3 , Stevo Todorčević 4, 5, 6
中文翻译:
具有非弱紧致生成的规范 Markuševič 基的 Asplund 空间
更新日期:2021-09-20
Advances in Mathematics ( IF 1.7 ) Pub Date : 2021-09-20 , DOI: 10.1016/j.aim.2021.108041 Petr Hájek 1 , Tommaso Russo 1, 2 , Jacopo Somaglia 3 , Stevo Todorčević 4, 5, 6
Affiliation
We construct an Asplund Banach space with a norming Markuševič basis such that is not weakly compactly generated. This solves a long-standing open problem from the early nineties, originally due to Gilles Godefroy. En route to the proof, we construct a peculiar example of scattered compact space, that also solves a question due to Wiesław Kubiś and Arkady Leiderman.
中文翻译:
具有非弱紧致生成的规范 Markuševič 基的 Asplund 空间
我们构造了一个 Asplund Banach 空间 以规范 Markuševič 为基础,使得 不是弱紧致生成。这解决了九十年代初一个长期存在的开放性问题,最初是由 Gilles Godefroy 提出的。途中要证明,我们建立的分散紧凑的空间特有的例子,这也解决了一个问题,由于库比什维斯拉夫阿尔卡季和Leiderman。