论文标题
空间中的准绿色基础$ \ ell_p $（$ 0 <p <1 $）是民主的
Quasi-greedy bases in the spaces $\ell_p$ ($0<p<1$) are democratic
论文作者
论文摘要
已知的Banach空间的列表，其线性几何形状决定了其准蛋白基础的（非线性）民主功能，以至于它们最终是民主的范围，降低到$ C_0 $，$ \ ell_2 $，以及所有可分开的$ \ nathcal $ \ nathcal {l} {l} _1 $ spaces。奇怪的是，这些是唯一的Banach空间，当它们具有无条件的基础时，它是独一无二的。我们在本文中的目的是研究非局部凸空间中的准绿色与民主之间的联系。我们证明，$ 0 <p <1 $（也有独特的无条件基础）的所有准杂乱基础都以$ \ ell_p $为单位，其基本功能与$（m^{1/p}）_ {m = 1}^\ infty $相同。我们开发的方法允许我们获得更多，即在任何可分开的$ \ Mathcal {l} _p $ -space，$ 0 <p <1 $的情况下都会发生相同的情况。
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 $c_0$, $\ell_2$, and all separable $\mathcal{L}_1$-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 nonlocally convex spaces. We prove that all quasi-greedy bases in $\ell_p$ for $0<p<1$ (which also has a unique unconditional basis) are democratic with fundamental function of the same order as $(m^{1/p})_{m=1}^\infty$. The methods we develop allow us to obtain even more, namely that the same occurs in any separable $\mathcal{L}_p$-space, $0<p<1$, with the bounded approximation property.
