A dichotomy for subsymmetric basic sequences with applications to Garling spaces

F. Albiac, J. L. Ansorena, S. Dilworth, D. Kutzarova
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引用次数: 4

Abstract

Our aim in this article is to contribute to the study of the structure of subsymmetric basic sequences in Banach spaces (even, more generally, in quasi-Banach spaces). For that we introduce the notion of positioning and develop new tools which lead to a dichotomy theorem that holds for general spaces with subsymmetric bases. As an illustration of how to use this dichotomy theorem we obtain the classification of all subsymmetric sequences in certain types of spaces. To be more specific, we show that Garling sequence spaces have a unique symmetric basic sequence but no symmetric basis and that these spaces have a continuum of subsymmetric basic sequences.
次对称基本序列的二分类及其在Garling空间中的应用
本文的目的是研究巴拿赫空间(甚至更一般地说是拟巴拿赫空间)中亚对称基序列的结构。为此,我们引入了定位的概念,并开发了新的工具,从而得出了一个适用于具有次对称基的一般空间的二分定理。为了说明如何使用这个二分定理,我们得到了在某些类型的空间中所有次对称序列的分类。更具体地说,我们证明了Garling序列空间有唯一的对称基序列但没有对称基,并且这些空间有次对称基序列的连续体。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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