Abstract The list of known Banach spaces whose linear geometry determines the (nonlinear) democracy functions of their quasi-greedy bases to the extent that they end up being democratic, reduces to c 0 , l 2 , and all separable L 1 -spaces. Oddly enough, these are the only Banach spaces that, when they have an unconditional basis, it is unique. Our aim in this paper is to study the connection between quasi-greediness and democracy of bases in non-locally convex spaces. We prove that all quasi-greedy bases in l p for 0 p 1 (which also has a unique unconditional basis) are democratic with fundamental function of the same order as ( m 1 / p ) m = 1 ∞ . The methods we develop allow us to obtain even more, namely that the same occurs in any separable L p -space, 0 p 1 , with the bounded approximation property.

中文翻译：

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ℓ (0 < p < 1) 中的准贪婪基是民主的

摘要 已知 Banach 空间的列表，其线性几何决定了它们的准贪婪基的（非线性）民主函数，直到它们最终是民主的，减少到 c 0 、l 2 和所有可分离的 L 1 空间。奇怪的是，这些是唯一的 Banach 空间，当它们具有无条件基时，它是唯一的。我们在本文中的目的是研究非局部凸空间中基的准贪婪和民主之间的联系。我们证明了 lp 中所有 0 p 1 的准贪婪基（它也有一个唯一的无条件基）是民主的，其基本函数与 ( m 1 / p ) m = 1 ∞ 的阶数相同。我们开发的方法使我们能够获得更多，即同样的情况发生在任何可分离的 L p 空间，0 p 1 中，具有有界近似属性。