弱贪婪算法及半贪婪与几乎贪婪 Markushevich 基的等价性
泛函分析
2021-10-15 v4
摘要
我们引入并研究了弱半贪婪系统的概念——其受半贪婪与分支半贪婪系统以及弱阈值集概念的启发——并证明在无限维 Banach 空间中的 Markushevich 基背景下，半贪婪、分支半贪婪、弱半贪婪以及几乎贪婪 Markushevich 基这些概念全部等价。这完成并扩展了 \cite{Berna2019}、\cite{Dilworth2003b} 和 \cite{Dilworth2012} 中的若干结果。我们还给出一个半贪婪系统例子，它既不是几乎贪婪的也不是 Markushevich 基，表明 Markushevich 条件不能从等价性结果中舍去。在某些情况下，我们获得了系统相应常数的改进上界。
引用
@article{arxiv.2004.06849,
title = {Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases},
author = {Miguel Berasategui and Silvia Lassalle},
journal= {arXiv preprint arXiv:2004.06849},
year = {2021}
}
备注
- The title is updated. - Definition 1.1 is fixed. - Several typos are fixed. - "the weak thresholding set" -> "the only weak thresholding set" (proof of Theorem 4.2). - An inaccuracy after equation (17) is corrected. - Some references are corrected, and some are added