Abstract
We continue the study undertaken in [1] of left democracy function $$h_l(N)=\inf_{\#\Lambda=N}||\sum_{n\in \Lambda_N}x_n||$$ of an unconditional basis in a Banach space $X$. We provide an example of a basis with $h_l$ non-doubling. Then we show that for bases with non-doubling $h_l$ the greedy projection is not optimal. Together with results from [1] improved by C. Cabrelli, G. Garrigós, E. Hernandez and U. Molter we get that the basis is greedy if and only if the greedy projection is optimal.
Citation
Przemysław Wojtaszczyk. "On left democracy function." Funct. Approx. Comment. Math. 50 (2) 207 - 214, June 2014. https://doi.org/10.7169/facm/2014.50.2.1
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