论文标题
在弱最大化特性上
On the Weak Maximizing Properties
论文作者
论文摘要
最近，已经引入了与规范运营商有关的新属性：最大化属性（WMP）。在本说明中，我们定义了IT的广义版本，它考虑了除弱拓扑以外的其他拓扑（主要是弱$^*$拓扑）。我们根据渐近均匀的平滑度和凸度的模量提供了新的足够条件，这意味着一对$（x，y）$具有一定的最大化属性。这种方法不仅允许我们（重新）获得直接的结果，即对$（\ ell_p，\ ell_q）$具有WMP，而且还提供了具有给定最大化属性的更多自然示例。
Quite recently, a new property related to norm-attaining operators has been introduced: the weak maximizing property (WMP). In this note, we define a generalised version of it considering other topologies than the weak one (mainly the weak$^*$ topology). We provide new sufficient conditions, based on the moduli of asymptotic uniform smoothness and convexity, which imply that a pair $(X,Y)$ enjoys a certain maximizing property. This approach not only allows us to (re)obtain as a direct consequence that the pair $(\ell_p,\ell_q)$ has the WMP, but also provides many more natural examples of pairs having a given maximizing property.
