NON-ERGODIC BANACH SPACES ARE NEAR HILBERT

被引：3

作者：

Cuellar Carrera, W. ^{[1
]}

机构：

[1] Univ Sao Paulo, Inst Matemat & Estat, R Matao 1010, Sao Paulo, SP, Brazil

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 370卷 / 12期

基金：

巴西圣保罗研究基金会;

关键词：

SUBSPACES;

D O I：

10.1090/tran/7319

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a non-ergodic Banach space must be near Hilbert. In particular, l(p), (2 < p < infinity) is ergodic. This reinforces the conjecture that l(2) is the only non-ergodic Banach space. As an application of our criterion for ergodicity, we prove that there is no separable Banach space which is complementably universal for the class of all subspaces of l(p), for 1 <= p <= 2. This solves a question left open by W. B. Johnson and A. Szankowski in 1976.

引用

页码：8691 / 8707

页数：17

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