I will talk about the theory of weak* sequential closures (weak* derived sets), which S. Banach and S. Mazurkiewicz started to develop in 1929-1932. I plan to describe the history of the topic and its applications. The main new result: for every nonreflexive Banach space X and every countable successor ordinal α, there exists a convex subset A in X* such that α is the least ordinal for which the weak* derived set of order α coincides with the weak* closure of A. This result extends the previously known results on weak* derived sets by Ostrovskii (2011) and Silber (2021).

The talk will be available under the link
Topic: Online Functional Analysis Seminar at IMPAN Time: JAN 18, 2022 03:00 PM Warsaw