算子空间上的优美满射
Nice surjections on spaces of operators
摘要：
如果一个有界线性算子的伴随算子保持对偶单位球的极值点，则称该算子是良算子。由于Labuschagne和Mascioni \cite{LM}的这种映射的空间紧算子的Hilbert空间的描述的动机，在这篇文章中，我们考虑一个描述的美好满射的${\mathcal K}(X,Y)$的Banach空间$X,Y$。给出了由复合算子给出良满射的充要条件。我们的结果意味着自动连续的这些映射相对于其他拓扑空间的运营商。我们还制定相应的结果${\mathcal L}(X,Y)$从而证明了类似的结果\cite{LM}的$L^p$（$1 <p \neq 2 <\infty$）空间。我们也制定的结果时，好的运营商不是规范形式，扩展和纠正的结果从\cite{KS}。
英文摘要：
A bounded linear operator is said to be nice if its adjoint preserves extreme points of the dual unit ball. Motivated by a description due to Labuschagne and Mascioni \cite{LM} of such maps for the space of compact operators on a Hilbert space, in this article we consider a description of nice surjections on ${\mathcal K}(X,Y)$ for Banach spaces $X,Y$. We give necessary and sufficient conditions when nice surjections are given by composition operators. Our results imply automatic continuity of these maps with respect to other topologies on spaces of operators. We also formulate the corresponding result for ${\mathcal L}(X,Y)$ thereby proving an analogue of the result from \cite{LM} for $L^p$ ($1 <p \neq 2 <\infty$) spaces. We also formulate results when nice operators are not of the canonical form, extending and correcting the results from \cite{KS}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
