论文标题
Lorentz序列空间的新的补充子空间，并应用了其封闭理想的晶格
A new complemented subspace for the Lorentz sequence spaces, with an application to its lattice of closed ideals
论文作者
论文摘要
我们表明，每个Lorentz序列空间$ d（\ textbf {w}，p）$允许1汇编的子空间$ y $与$ \ ell_p $不同，并且包含$ d（\ textbf {w}，p）$的no isomorph。在一般情况下，这只是$ d（\ textbf {w}，p）$中的第二个非平凡补充子空间。 We also give an explicit representation of $Y$ in the special case $\textbf{w}=(n^{-θ})_{n=1}^\infty$ ($0<θ<1$) as the $\ell_p$-sum of finite-dimensional copies of $d(\textbf{w},p)$.作为一个应用程序，我们在$ \ Mathcal {l}的封闭理想的晶格中找到了第六个不同的元素（d（\ textbf {w}，p），p））$，其中只有五个以前在一般情况下才知道。
We show that every Lorentz sequence space $d(\textbf{w},p)$ admits a 1-complemented subspace $Y$ distinct from $\ell_p$ and containing no isomorph of $d(\textbf{w},p)$. In the general case, this is only the second nontrivial complemented subspace in $d(\textbf{w},p)$ yet known. We also give an explicit representation of $Y$ in the special case $\textbf{w}=(n^{-θ})_{n=1}^\infty$ ($0<θ<1$) as the $\ell_p$-sum of finite-dimensional copies of $d(\textbf{w},p)$. As an application, we find a sixth distinct element in the lattice of closed ideals of $\mathcal{L}(d(\textbf{w},p))$, of which only five were previously known in the general case.
