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On weak sequential completeness of spaces where weakly compact sets are super weakly compact
Zdeněk Silber
We show that every Banach space in which weakly compact sets are super weakly compact in automatically weakly sequentially complete answering a question by Silber (2024). In the pr…
Countably tight dual ball with a nonseparable measure
Piotr Koszmider, Zdeněk Silber
We construct a compact Hausdorff space such that the space of Radon probabiblity measures on considered with the weak topology (induced from the space of continu…
On subspaces whose weak* derived sets are proper and norm dense
Zdeněk Silber
We study long chains of iterated weak* derived sets, that is sets of all weak* limits of bounded nets, of subspaces with the additional property that the penultimate weak* derived…
Quantification of Banach-Saks properties of higher orders
Zdeněk Silber
We investigate possible quantifications of Banach-Saks sets and weak Banach-Saks sets of higher orders and their relations to other quantities. We prove a quantitative version of t…
Weak derived sets of convex sets in duals of non-reflexive spaces
Zdeněk Silber
We investigate weak derived sets, that is the sets of weak limits of bounded nets, of convex subsets of duals of non-reflexive Banach spaces and their possible iterations.…