论文标题
Kalton-Peck空间上的运营商$ Z_2 $
Operators on the Kalton-Peck space $Z_2$
论文作者
论文摘要
我们从各种观点上研究了Kalton-Peck Banach空间$ Z_2 $的操作员：矩阵表示，示例，光谱属性和操作员理想。例如，我们证明存在非紧密的，严格的奇异操作员作用于$ z_2 $，但其中两个的产物是紧凑的操作员。 Among applications, we show that every copy of $Z_2$ in $Z_2$ is complemented, and each semi-Fredholm operator on $Z_2$ has complemented kernel and range, the space $Z_2$ is $Z_2$-automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schetchman about strictly singular perturbations of operators on $Z_2$.
We study operators on the Kalton-Peck Banach space $Z_2$ from various points of view: matrix representations, examples, spectral properties and operator ideals. For example, we prove that there are non-compact, strictly singular operators acting on $Z_2$, but the product of two of them is a compact operator. Among applications, we show that every copy of $Z_2$ in $Z_2$ is complemented, and each semi-Fredholm operator on $Z_2$ has complemented kernel and range, the space $Z_2$ is $Z_2$-automorphic and we give a partial solution to a problem of Johnson, Lindenstrauss and Schetchman about strictly singular perturbations of operators on $Z_2$.
