论文标题
从长序列空间上的操作员代数的过滤性同态是自动注入性的
Surjective homomorphisms from algebras of operators on long sequence spaces are automatically injective
论文作者
论文摘要
我们研究了从$ \ mathscr {b}（x）$，（有限的，线性）运算符的代数，$ x $，$ x $，$ \ mathscr {b}（y）$的自动注射率。 $ \ ell _ {\ infty}^c（λ）$和$ \ ell_p（λ）$（$ 1 \ leqslant p <\ infty $），$ y $是任意的。 \ textit {en ute}以证明这些空间确实享受了这样的属性，我们对任何上述的Banach空间的操作员代数的双面理想进行了分类，这些空间相对于“顺序强型操作员拓扑”而封闭。
We study automatic injectivity of surjective algebra homomorphisms from $\mathscr{B}(X)$, the algebra of (bounded, linear) operators on $X$, to $\mathscr{B}(Y)$, where $X$ is one of the following \emph{long} sequence spaces: $c_0(λ)$, $\ell_{\infty}^c(λ)$, and $\ell_p(λ)$ ($1 \leqslant p < \infty$) and $Y$ is arbitrary. \textit{En route} to the proof that these spaces do indeed enjoy such a property, we classify two-sided ideals of the algebra of operators of any of the aforementioned Banach spaces that are closed with respect to the `sequential strong operator topology'.
