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arXiv · 2004.06849

Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases

Miguel Berasategui·Silvia Lassalle
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Abstract

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.

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Miguel Berasategui, Silvia Lassalle. 2020-04-15. Weak greedy algorithms and the equivalence between semi-greedy and almost greedy Markushevich bases. https://arxiv.org/abs/2004.06849

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