On ultrapowers of Banach spaces of type L∞

被引：7

作者：

Aviles, Antonio ^{[1
]}

Gonzalez, Manuel ^{[2
]}

Cabello Sanchez, Felix ^{[3
]}

Castillo, Jesus M. F. ^{[3
]}

Moreno, Yolanda ^{[4
]}

机构：

[1] Univ Murcia, Dept Matemat, E-30100 Murcia, Spain

[2] Univ Cantabria, Dept Matemat, Santander 39071, Spain

[3] Univ Extremadura, Dept Matemat, E-06071 Badajoz, Spain

[4] Univ Extremadura, Escuela Politecn, Caceres 10071, Spain

来源：

FUNDAMENTA MATHEMATICAE | 2013年 / 222卷 / 03期

关键词：

ultraproducts of Banach spaces; L-infinity spaces; NONSTANDARD HULLS; ULTRAPRODUCTS;

D O I：

10.4064/fm222-3-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that no ultraproduct of Banach spaces via a countably incomplete ultrafilter can contain c(0) complemented. This shows that a "result" widely used in the theory of ultraproducts is wrong. We then amend a number of results whose proofs have been infected by that statement. In particular we provide proofs for the following statements: (i) All M-spaces, in particular all C(K)-spaces, have ultrapowers isomorphic to ultrapowers of c(0), as also do all their complemented subspaces isomorphic to their square. (ii) No ultrapower of the Gurarii space can be complemented in any M-space. (iii) There exist Banach spaces not complemented in any C(K)-space having ultrapowers isomorphic to a C(K)-space.

引用

页码：195 / 212

页数：18

共 41 条

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