弱贪婪算法及半贪婪和几乎贪婪Markushevich基的等价性
Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases
摘要：
我们引入并研究了弱半贪婪系统的概念--它是受半贪婪系统、分支半贪婪系统和弱阈值集概念的启发--并证明了在无限维巴拿赫空间中的Markushevich基的上下文中，\textit{ semi-greedy, branch semi-greedy, weak semi-greedy, and almost greedy} Markushevich基的概念都是等价的.这完成并推广了\cite{Berna2019}、\cite{Dilworth2003b}和\cite{Dilworth2012}的一些结果。我们还展示了一个半贪婪系统的例子，既不是几乎贪婪也不是Markushevich基础，表明Markushevich条件不能从等价结果中删除。在某些情况下，我们得到了系统相应常数的改进的上界。
英文摘要：
We introduce and study the notion of weak semi-greedy systems -which is inspired in the concepts of semi-greedy and Branch semi-greedy systems and weak thresholding sets-, and prove that in the context Markushevich bases in infinite dimensional Banach spaces, the notions of \textit{ semi-greedy, branch semi-greedy, weak semi-greedy, and almost greedy} Markushevich bases are all equivalent. This completes and extends some results from \cite{Berna2019}, \cite{Dilworth2003b}, and \cite{Dilworth2012}. We also exhibit an example of a semi-greedy system that is neither almost greedy nor a Markushevich basis, showing that the Markushevich condition cannot be dropped from the equivalence result. In some cases, we obtain improved upper bounds for the corresponding constants of the systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
