Polish spaces of Banach spaces

Abstract

We present and thoroughly study natural Polish spaces of separable Banach spaces. These spaces are defined as spaces of norms, resp. 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 different 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.

Based on the referees' comments, the original submission has been split into two parts. The new version is the first part of the split. The second one is arXiv:2204.06834 [math.FA]

References in corpus (2)

• Polish spaces of Banach spaces
• Complexity of distances: Reductions of distances between metric and Banach spaces

Cited by in corpus (5)

• Polish spaces of Banach spaces
• Polish spaces of Banach spaces. Complexity of isometry and isomorphism classes
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