论文标题
多项式理想的补充子空间
Complemented subspaces of polynomial ideals
论文作者
论文摘要
给定多项式理想$ \ Mathcal {J} \ Circ \ Mathcal {p}（^{n} e; f）$，我们证明，如果$ \ Mathcal {J} \ Circ \ Mathcal {p}（p} {p}（^n} e; f） $ \ Mathcal {J} \ Circ \ Mathcal {p}（^{n} e; f）$在$ \ Mathcal {p}（^{n} e; f）$中不补充，每个封闭的操作员的$ \ {n} $ n \ in \ mathbb {n} $。同样，我们表明，如果$ \ wideHat {（\ Mathcal {J} \ Circ \ Mathcal {l}） $ \ wideHat {（\ Mathcal {J} \ Circ \ Mathcal {l}）^{fac}}}（^{n} e; f）$在$ \ Mathcal {p}（p}（p}（^n} e； \ Mathcal {l} _ {k} $和每个$ n> 1 $。当$ \ Mathcal {J} = \ Mathcal {l} _ {k} $，这些结果概括了几位作者的结果\ cite {lew}，\ cite {em}，\ cite {kalton}，\ cite {kalton}，\ cite {ioAana}，\ cite {ioana}，\ cite {sergio {sergio {sergio {sergio}，等。
Given the polynomial ideal $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$, we prove that if $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$ contains an isomorphic copy of $c_{0}$, then $\mathcal{J}\circ\mathcal{P} (^{n}E; F)$ is not complemented in $\mathcal{P} (^{n}E; F)$ for every closed operator ideal $\mathcal{J}\subset \mathcal{L}_{K}$ and every $n\in\mathbb{N}$. Likewise we show that if $\widehat{(\mathcal{J}\circ\mathcal{L})^{fac}}(^{n}E;F)$ contains an isomorphic copy of $c_{0}$, then $\widehat{(\mathcal{J}\circ\mathcal{L})^{fac}}(^{n}E;F)$ is not complemented in $\mathcal{P}(^{n}E; F)$ for every closed operator ideal $\mathcal{J}\subset \mathcal{L}_{K}$ and every $n>1$. When $\mathcal{J}=\mathcal{L}_{K}$, these results generalizes results of several authors \cite{LEW},\cite{EM},\cite{KALTON},\cite{IOANA},\cite{SERGIO}, among others.
