ON THE SEPARABLE QUOTIENT PROBLEM FOR BANACH SPACES

被引：8

作者：

Ferrando, Juan C. ^{[1
]}

Kakol, Jerzy ^{[2
]}

Lopez-Pellicer, Manuel ^{[3
,4
]}

Sliwa, Wieslaw ^{[5
]}

机构：

[1] Univ Miguel Hernandez, Ctr Invest Operat, Edificio Torretamarit,Avda Univ, E-03202 Elche, Alicante, Spain

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-61614 Poznan, Poland

[3] Univ Politecn Valencia, Dept Matemat Aplicada, E-46022 Valencia, Spain

[4] Univ Politecn Valencia, IMPA, E-46022 Valencia, Spain

[5] Univ Rzeszow, Fac Math & Nat Sci, PL-35310 Rzeszow, Poland

来源：

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2018年 / 59卷 / 02期

关键词：

Banach space; barrelled space; separable quotient; vector-valued function space; linear operator space; vector measure space; tensor product; Radon-Nikodym property;

D O I：

10.7169/facm/1704

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of infinite-dimensional separable quotients in some Banach spaces of vector-valued functions, linear operators and vector measures. Most of the presented results are consequences of known facts, some of them relative to the presence of complemented copies of the classic sequence spaces co and l(p), for 1 <= p <= infinity. Also recent results of Argyros, Dodos, Kanellopoulos [1] and Sliwa [64] are provided. This makes our presentation supplementary to a previous survey (1997) due to Mujica.

引用

页码：153 / 173

页数：21

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