Descriptive complexity of some isomorphism classes of Banach spaces

被引：7

作者：

Godefroy, Gilles ^{[1
]}

Saint-Raymond, Jean ^{[1
]}

机构：

[1] Univ Pierre & Marie Curie Univ Paris 06, Univ Pierre & Marie Curie Paris 6, Sorbonne Univ, Inst Math Jussieu Paris Rive Gauche,CNRS, Boite 186,4 Pl Jussieu, F-75252 Paris 05, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2018年 / 275卷 / 04期

关键词：

Banach spaces; Borel classes; Descriptive complexity; SUBSPACES; QUOTIENTS; BOREL; LP;

D O I：

10.1016/j.jfa.2018.01.018

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a topological frame in which it is possible to estimate the complexity of some Borel families of separable Banach spaces. We use this frame for evaluating the complexity of the isomorphism class of the Hilbert space l(2), of certain asymptotically Hilbertian spaces, and of the l(p) spaces under the condition 1 < p < infinity. The complexity appears to increase with the distance to the Hilbert space. Commented open problems conclude the article. (C) 2018 Published by Elsevier Inc.

引用

页码：1008 / 1022

页数：15

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