Approximation of integration maps of vector measures and limit representations of Banach function spaces

被引：1

作者：

Jimenez Fernandez, Eduardo ^{[1
]}

Sanchez Perez, Enrique A. ^{[2
]}

Werner, Dirk ^{[3
]}

机构：

[1] Univ Jaume 1, Dept Econ, Campus Riu Sec S-N, Castellon de La Plana 12071, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Camino Vera S-N, E-46022 Valencia, Spain

[3] Free Univ Berlin, Fachbereich Math & Informat, Arnimallee 6, D-14195 Berlin, Germany

来源：

ANNALES POLONICI MATHEMATICI | 2017年 / 120卷 / 01期

关键词：

vector measures; integration map; Daugavet property; REARRANGEMENT-INVARIANT SPACES; DAUGAVET PROPERTY; NUMERICAL INDEX; OPERATORS; CENTERS;

D O I：

10.4064/ap170407-21-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study whether or not the integration maps of vector measures can be computed as pointwise limits of their finite rank Radon Nikodym derivatives. The positive cases are obtained by using the circle of ideas related to the approximation property for Banach spaces. The negative ones are given by means of an appropriate use of the Daugavet property. As an application, we analyse when the norm in a space L-1(m) of integrable functions can be computed as a limit of the norms of the spaces of integrable functions with respect to the Radon-Nikodym derivatives of m.

引用

页码：63 / 81

页数：19

共 15 条

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