关于弱极大化性质
On the Weak Maximizing Properties
摘要：
最近，一个新的性质有关的范数达到运营商已被引入：弱极大化性质（WMP）。在这篇笔记中，我们定义了一个广义版本，它考虑到其他的拓扑比弱的（主要是弱$^*$拓扑）。我们提供了新的充分条件，基于模的渐近一致光滑性和凸性，这意味着一对$(X,Y)$享有一定的极大化性质。这种方法不仅使我们能够（重新）获得作为一个直接的结果，对$(\ell_p,\ell_q)$具有WMP，但也提供了许多更自然的例子，对具有给定的最大化属性。
英文摘要：
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.
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