On constructions of strong and uniformly minimal M-bases in Banach spaces

被引：1

作者：

Vershynin, R ^{[1
]}

机构：

[1] Univ Jena, Fak Math & Informat, D-07743 Jena, Germany

来源：

ARCHIV DER MATHEMATIK | 2000年 / 74卷 / 01期

关键词：

Banach Space; Positive Answer; Natural Class; Standard Transformation;

D O I：

10.1007/PL00000409

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find a natural class of transformations ("flattened perturbations") of a norming M-basis in a Banach space X, which give a strong norming M-basis in X. This simplifies and generalizes the positive answer to the "strong M-basis problem" solved by P. Terenzi. We also show that in general one cannot achieve uniformly minimality applying standard transformations to a given norming M-basis, despite of the existence in X a uniformly minimal strong M-bases.

引用

页码：50 / 60

页数：11

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