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 \(\hbox {weak}^*\) 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.

最近，引入了与规范获得算子相关的新属性：弱最大化属性（WMP）。在这篇笔记中，我们定义了一个广义版本，考虑到除弱拓扑之外的其他拓扑（主要是\(\hbox {weak}^*\)拓扑）。我们基于渐近均匀平滑度和凸度的模数提供了新的充分条件，这意味着一对 ( X ,  Y ) 享有一定的最大化属性。这种方法不仅允许我们（重新）获得对\((\ell _p,\ell _q)\)具有 WMP的直接结果，而且还提供了许多具有给定最大化属性的对的自然示例。