On the existence of almost greedy bases in Banach spaces

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Greedy approximation (2008, background): “The following proposition follows from the proof of Theorem 3.3 of Dilworth et al. (2003) (see Theorem 1.4.10 below).”
Greedy approximation for biorthogonal systems in quasi-Banach spaces (2019, methodology): “in [32] on the comparison between the “best greedy error” of the greedy algorithm with its “best almost-greedy error.”