2 citations · 4 across the 5 of their papers we have counts for
17 papers
Continuity of coordinate functionals of filter bases in Banach spaces
Noé de Rancourt, Tomasz Kania, Jarosław Swaczyna
We prove that the coordinate functionals associated with filter bases in Banach spaces are continuous as long as the underlying filter is analytic. This removes the large-cardinal…
Quantifying shrinking and boundedly complete bases
Dongyang Chen, Tomasz Kania, Yingbin Ruan
We investigate possible quantifications of R. C. James' classical work on bases and reflexivity of Banach spaces. By introducing new quantities measuring how far a basic sequence i…
Grothendieck spaces: the landscape and perspectives
Manuel González, Tomasz Kania
In 1973, Diestel published his seminal paper `Grothendieck spaces and vector measures' that drew a connection between Grothendieck spaces (Banach spaces for which weak- and weak*-s…
Quantifying properties () and ()
Dongyang Chen, Tomasz Kania, Yingbin Ruan
A Banach space has \textit{property }, whenever every weak* null sequence in the dual space admits a convex block subsequence so that $\langle f_{n}…
Invariant means on Abelian groups capture complementability of Banach spaces in their second duals
Adam P. Goucher, Tomasz Kania
Let be a Banach space. Then is complemented in the bidual if and only if there exists an invariant mean with respect to a free Abelian gro…
Large cardinals and continuity of coordinate functionals of filter bases in Banach spaces
Tomasz Kania, Jarosław Swaczyna
Assuming the existence of certain large cardinal numbers, we prove that for every projective filter over the set of natural numbers, -bases in Banach spac…