ON λ-STRICT IDEALS IN BANACH SPACES

被引：3

作者：

Abrahamsen, Trond A. ^{[1
]}

Nygaard, Olav ^{[1
]}

机构：

[1] Univ Agder, Dept Math, N-4604 Kristiansand, Norway

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2011年 / 83卷 / 02期

关键词：

strict ideal; u-ideal; VN-subspace; UNCONDITIONAL IDEALS; U-IDEALS; OPERATORS;

D O I：

10.1017/S0004972710001735

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define and study A-strict ideals in Banach spaces, which for lambda = 1 means strict ideals. Strict u-ideals in their biduals are known to have the unique ideal property; we prove that so also do A-strict u-ideals in their biduals, at least for lambda > 1/2. An open question, posed by Godefroy etal. ['Unconditional ideals in Banach spaces', Studia Math. 104 (1993), 13-59] is whether the Banach space X is a u-ideal in Ba(X), the Baire-one functions in X**, exactly when kappa(u) (X) = 1; we prove that if kappa(u)(X) = I then X is a strict u-ideal in Ba(X), and we establish the converse in the separable case.

引用

页码：231 / 240

页数：10