5 papers · 1 filter
Bourgain-uo sequential completeness in vector lattices
Tomasz Kania, Jarosław Swaczyna
We revisit Bourgain's 1981 counterexample to the sequential completeness of the `pointwise plus domination' convergence on from the perspective of vector lattices. In this…
The -property of a Banach space along a filter
Tomasz Kania, Jarosław Swaczyna
We examine the analyticity of the class of separable Banach spaces possessing the -property, defined in terms of convergence along a filter. Our results establish that this clas…
Zoo of ideal Schauder basis
Adam Kwela, Jarosław Swaczyna
We investigate the notion of filter (equivalently: ideal) Schauder basis of a Banach space. We do so by providing bunch of new examples of such bases that are not the standard ones…
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…
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…