In this paper, we continue the study of Berkani's property $\left(U{W}_{\mathrm{\Pi }}\right)$ introduced in [Berkani M, Kachad M. New Browder and Weyl type theorems. Bull Korean Math Soc. 2015;52:439–452.], in connection with other Weyl-type theorems. Moreover, we give counterexamples to show that some recent results related to this property, which are announced and proved by P. Aiena and M. Kachad in [Aiena P, Kachad M. Property $\left(U{W}_{\mathrm{\Pi }}\right)$ and perturbations. Ann Funct Anal. 2020;11:29–46.] are false. Furthermore, we specify the mistakes committed in each of them and we give the correct versions. We also give a global note on the paper [Jayanthi N, Vasanthakumar P. A new Browder type property. Inter J Math Anal. 2020;14:1–11].

在本文中，我们继续研究 Berkani 的性质$\left(üW_{\mathrm{\pi }}\right)$在 [Berkani M, Kachad M. New Browder 和 Weyl 类型定理中介绍。公牛韩国数学 Soc。2015;52:439–452.]，与其他 Weyl 型定理有关。此外，我们给出反例来说明 P. Aiena 和 M. Kachad 在 [Aiena P, Kachad M. Property$\left(üW_{\mathrm{\pi }}\right)$和扰动。安功能肛门。2020;11:29–46.] 是错误的。此外，我们详细说明了其中每一个所犯的错误，并给出了正确的版本。我们还在论文 [Jayanthi N, Vasanthakumar P. A new Browder type property. Inter J 数学肛门。2020；14：1-11]。