论文标题
通用的ACK结构和达到规范运算符的密度
A generalized ACK structure and the denseness of norm attaining operators
论文作者
论文摘要
受Cascales等人最近的工作的启发，我们在Banach空间上引入了广义的ACK结构概念。使用该属性，我们通过准Ack结构称之为，我们能够在范围空间上扩展已知的通用属性，以涉及到达到规范的运算符的密度。我们为空间的准ACK结构提供了足够的条件，并为准Ack结构的稳定性提供了结果。结果，我们提出了满足（Lindenstrauss）财产B $^k $的新例子，这是以前尚不清楚的。我们还证明，在某些情况下，在注射量张量的产品下，财产B $^K $是稳定的。此外，还讨论了某些矢量值霍明型功能的ACK结构，从而为某些操作员理想提供了通用BPB范围空间的新示例。
Inspired by the recent work of Cascales et al., we introduce a generalized concept of ACK structure on Banach spaces. Using this property, which we call by the quasi-ACK structure, we are able to extend known universal properties on range spaces concerning the density of norm attaining operators. We provide sufficient conditions for quasi-ACK structure of spaces and results on the stability of quasi-ACK structure. As a consequence, we present new examples satisfying the (Lindenstrauss) property B$^k$, which have not been known previously. We also prove that property B$^k$ is stable under injective tensor products in certain cases. Moreover, ACK structure of some Banach spaces of vector-valued holomorphic functions is also discussed, leading to new examples of universal BPB range spaces for certain operator ideals.
