Polish spaces of Banach spaces

0558103 - MÚ 2023 RIV GB eng J - Journal Article
Cúth, M. - Doležal, Martin - Doucha, Michal - Kurka, Ondřej
Polish spaces of Banach spaces.
Forum of Mathematics, Sigma. Roč. 10, May (2022), č. článku e26. E-ISSN 2050-5094
R&D Projects: GA ČR(CZ) GA17-27844S; GA ČR(CZ) GJ19-05271Y; GA ČR GA17-00941S
Institutional support: RVO:67985840
Keywords : Banach spaces * descriptive set theory * Baire category
OECD category: Pure mathematics
Impact factor: 1.7, year: 2022
Method of publishing: Open access
https://doi.org/10.1017/fms.2022.16

We present and thoroughly study natural Polish spaces of separable Banach spaces. These spaces are defined as spaces of norms, respectively pseudonorms, on the countable infinite-dimensional rational vector space. We provide an exhaustive comparison of these spaces with admissible topologies recently introduced by Godefroy and Saint-Raymond and show that Borel complexities differ little with respect to these two topological approaches. We investigate generic properties in these spaces and compare them with those in admissible topologies, confirming the suspicion of Godefroy and Saint-Raymond that they depend on the choice of the admissible topology.
Permanent Link: http://hdl.handle.net/11104/0331901