Narrow operators and the Daugavet property for ultraproducts

被引：22

作者：

Bilik, D ^{[1
]}

Kadets, V

Shvidkoy, R

Werner, D

机构：

[1] Univ Missouri, Dept Math, Columbia, MO 65211 USA

[2] Kharkov Natl Univ, Fac Mech & Math, UA-61077 Kharkov, Ukraine

[3] Univ Texas, Dept Math, Austin, TX 78712 USA

[4] Free Univ Berlin, Dept Math, D-14195 Berlin, Germany

来源：

POSITIVITY | 2005年 / 9卷 / 01期

关键词：

Daugavet property; narrow operator; strong Daugavet operator; ultraproducts of Banach spaces;

D O I：

10.1007/s11117-003-9339-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that if T is a narrow operator ( for the definition see below) on X = X-1 +(1) X-2 or X = X-1 +(infinity) X-2, then the restrictions to X-1 and X-2 are narrow and conversely. We also characterise by a version of the Daugavet property for positive operators on Banach lattices which unconditional sums of Banach spaces inherit the Daugavet property, and we study the Daugavet property for ultraproducts.

引用

页码：45 / 62

页数：18

共 10 条

[1]

Abramovich Y., 1991, J. Oper. Theory, V25, P331

[2]

Beauzamy B., 2011, INTRO BANACH SPACES

[3]

Bilik D, 2002, ILLINOIS J MATH, V46, P421

[4] MARTINGALES VALUED IN CERTAIN SUBSPACES OF L1 [J].