论文标题
$ l_2 $的chauder基础，由非负功能组成
A Schauder basis for $L_2$ consisting of non-negative functions
论文作者
论文摘要
我们证明$ L_2（\ Mathbb {r}）$包含非负函数的schauder基础。同样，$ l_p（\ mathbb {r}）$包含一个非阴性函数的基本序列，从而嵌入$ l_p（\ mathbb {r}）$嵌入到序列的封闭范围中。我们还证明，如果$ x $是具有有限近似属性的可分开的Banach空间，则具有$ x $的$ x $中的任何设置都包含$ x $的准巴斯（Schauder框架）。此外，如果$ x $是带有bibasis的可分离的Banach晶格，则具有$ x $的任何设置，具有密度跨度的$ x $都包含U-Frame。
We prove that $L_2(\mathbb{R})$ contains a Schauder basis of non-negative functions. Similarly, $L_p(\mathbb{R})$ contains a Schauder basic sequence of non-negative functions such that $L_p(\mathbb{R})$ embeds into the closed span of the sequence. We prove as well that if $X$ is a separable Banach space with the bounded approximation property, then any set in $X$ with dense span contains a quasi-basis (Schauder frame) for $X$. Furthermore, if $X$ is a separable Banach lattice with a bibasis then any set in $X$ with dense span contains a u-frame.
