On weak compactness of bounded sets in Banach and locally convex spaces

• Date: 2000
• Main Authors: Kogut, P. I., Mel'nik, V. S., Когут, П. И., Мельник, В. С.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2000
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4467
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate the compactness of one class of bounded subsets in Banach and locally convex spaces. We obtain a generalization of the Banach-Alaoglu theorem to a class of subsets that are not polars of convex balanced neighborhoods of zero.