Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772249 | Journal of Functional Analysis | 2017 | 24 Pages |
Abstract
A topological setting is defined to study the complexities of the relation of equivalence of embeddings (or “position”) of a Banach space into another and of the relation of isomorphism of complex structures on a real Banach space. The following results are obtained: a) if X is not uniformly finitely extensible, then there exists a space Y for which the relation of position of Y inside X reduces the relation E0 and therefore is not smooth; b) the relation of position of âp inside âp, or inside Lp, pâ 2, reduces the relation E1 and therefore is not reducible to an orbit relation induced by the action of a Polish group; c) the relation of position of a space inside another can attain the maximum complexity Emax; d) there exists a subspace of Lp, 1â¤p<2, on which isomorphism between complex structures reduces E1 and therefore is not reducible to an orbit relation induced by the action of a Polish group.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Razvan Anisca, Valentin Ferenczi, Yolanda Moreno,