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Generalized-lush spaces revisited
Annals of Functional Analysis ( IF 1.2 ) Pub Date : 2020-01-01 , DOI: 10.1007/s43034-019-00029-w
V. Kadets , O. Zavarzina

We study geometric properties of GL-spaces. We demonstrate that every finite-dimensional GL-space is polyhedral; that in dimension 2 there are only two, up to isometry, GL-spaces, namely the space whose unit sphere is a square (like $\ell_\infty^2$ or $\ell_1^2$) and the space whose unit sphere is an equilateral hexagon. Finally, we address the question what are the spaces $E = (\R^n, \|\cdot\|_E)$ with absolute norm such that for every collection $X_1, \ldots, X_n$ of GL-spaces their $E$-sum is a GL-space.

中文翻译:

重新审视广义郁郁葱葱的空间

我们研究 GL 空间的几何特性。我们证明了每个有限维 GL 空间都是多面体;在维度 2 中只有两个,直到等距,GL 空间,即单位球体是正方形的空间(如 $\ell_\infty^2$ 或 $\ell_1^2$)和单位球体的空间是等边六边形。最后,我们解决了具有绝对范数的空间 $E = (\R^n, \|\cdot\|_E)$ 的问题,使得对于 GL 空间的每个集合 $X_1, \ldots, X_n$ E$-sum 是一个 GL 空间。
更新日期:2020-01-01
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