An example regarding Kalton's paper "Isomorphisms between spaces of vector-valued continuous functions"
Functional Analysis
2021-05-28 v2 General Topology
Abstract
The paper alluded to in the title contains the following striking result: Let be the unit interval and the Cantor set. If is a quasi Banach space containing no copy of which is isomorphic to a closed subspace of a space with a basis and is linearly homeomorphic to , then is locally convex, i.e., a Banach space. It is shown that Kalton result is sharp by exhibiting non locally convex quasi Banach spaces X with a basis for which and are isomorphic. Our examples are rather specific and actually in all cases X is isomorphic to if is a metric compactum of finite covering dimension.
Cite
@article{arxiv.2102.02102,
title = {An example regarding Kalton's paper "Isomorphisms between spaces of vector-valued continuous functions"},
author = {Félix Cabello Sánchez},
journal= {arXiv preprint arXiv:2102.02102},
year = {2021}
}
Comments
4 pages