论文标题
足够家庭产生的Banach空间中的三角洲点
Delta-points in Banach spaces generated by adequate families
论文作者
论文摘要
我们在Banach空间中研究三角点$ h _ {\ Mathcal {a}，P}，由充分家庭生成的$ \ Mathcal A $ $ 1 \ le P <\ infty $。在这种情况下，家族$ \ Mathcal a $是常规的，$ p = 1，$这些空间被称为组合Banach空间。当$ p> 1 $时，我们证明$ h _ {\ mathcal {a}，p} $也不包含delta-points。在额外的假设是$ \ Mathcal a $是常规的，我们证明当$ p = 1时相同。如果$ \ mathcal a $由有限集组成，只有我们能够排除$ h _ {\ Mathcal {a}，1}，1} $和DAUGAVET-POINTS中的Delta点的存在。 我们还表明，如果$ h _ {\ Mathcal {a}，1} $是多面体，那么它是（i）-polyhedral或（v）-polyhedral（从FONF和VESELý的意义上）。
We study delta-points in Banach spaces $h_{\mathcal{A},p}$ generated by adequate families $\mathcal A$ where $1 \le p < \infty$. In the case the familiy $\mathcal A$ is regular and $p=1,$ these spaces are known as combinatorial Banach spaces. When $p > 1$ we prove that neither $h_{\mathcal{A},p}$ nor its dual contain delta-points. Under the extra assumption that $\mathcal A$ is regular, we prove that the same is true when $p=1.$ In particular the Schreier spaces and their duals fail to have delta-points. If $\mathcal A$ consists of finite sets only we are able to rule out the existence of delta-points in $h_{\mathcal{A},1}$ and Daugavet-points in its dual. We also show that if $h_{\mathcal{A},1}$ is polyhedral, then it is either (I)-polyhedral or (V)-polyhedral (in the sense of Fonf and Veselý).
