拟banach空间中双正交系统的贪心逼近

IF 1.5 3区数学 Q1 MATHEMATICS

Dissertationes Mathematicae Pub Date : 2019-03-27 DOI:10.4064/DM817-11-2020

F. Albiac, J. L. Ansorena, P. M. Berná, P. Wojtaszczyk

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引用次数: 52

摘要

这项工作中解决的一般问题是从函数分析的角度，系统地研究了拟Banach空间中一般双正交系统（也称为Markushevich基）的阈值贪婪算法。在这个综合框架中，我们重新审视了贪婪基、拟贪婪基和几乎贪婪基的概念，并提供了这些类型的基的相应特征的（非平凡的）扩展。作为我们工作的副产品，出现了新的特性，并仔细讨论了它们之间的关系。

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Greedy approximation for biorthogonal systems in quasi-Banach spaces

The general problem addressed in this work is the development of a systematic study of the thresholding greedy algorithm for general biorthogonal systems (also known as Markushevich bases) in quasi-Banach spaces from a functional-analytic point of view. We revisit the concepts of greedy, quasi-greedy, and almost greedy bases in this comprehensive framework and provide the (nontrivial) extensions of the corresponding characterizations of those types of bases. As a by-product of our work, new properties arise, and the relations amongst them are carefully discussed.

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来源期刊

Dissertationes Mathematicae 数学-数学

CiteScore

2.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： DISSERTATIONES MATHEMATICAE publishes long research papers (preferably 50-100 pages) in any area of mathematics. An important feature of papers accepted for publication should be their utility for a broad readership of specialists in the domain. In particular, the papers should be to some reasonable extent self-contained. The paper version is considered as primary. The following criteria are taken into account in the reviewing procedure: correctness, mathematical level, mathematical novelty, utility for a broad readership of specialists in the domain, language and editorial aspects. The Editors have adopted appropriate procedures to avoid ghostwriting and guest authorship.