论文标题
贪婪算法和半绿色和几乎贪婪的马库什维奇基地之间的等效性
Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases
论文作者
论文摘要
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都是等效的。这完成并扩展了一些结果，从\ cite {berna2019}，\ cite {dilworth2003b}和\ cite {dilworth2012}。我们还展示了一个半怪兽系统的示例，该系统几乎是贪婪也不是Markushevich的基础，这表明Markushevich条件不能从等价结果中删除。在某些情况下，我们为系统的相应常数获得了改进的上限。
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.
