| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, IMECC, BR-13083970 Campinas, SP - Brazil
[2] Univ Granada, Fac Ciencias, Dept Anal Matemat, E-18071 Granada - Spain
[3] Inst Matematyki Politech Lodzkiej, PL-90924 Lodz - Poland
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | Israel Journal of Mathematics; v. 190, n. 1, p. 93-110, AUG 2012. |
| Web of Science Citations: | 11 |
| Abstract | |
We consider the question whether there exists a Banach space X of density continuum such that every Banach space of density at most continuum isomorphically embeds into X (called a universal Banach space of density c). It is well known that a{''}{''}(a)/c (0) is such a space if we assume the continuum hypothesis. Some additional set-theoretic assumption is indeed needed, as we prove in the main result of this paper that it is consistent with the usual axioms of set-theory that there is no universal Banach space of density c. Thus, the problem of the existence of a universal Banach space of density c is undecidable using the usual axioms of set-theory. We also prove that it is consistent that there are universal Banach spaces of density c, but a{''}{''}(a)/c (0) is not among them. This relies on the proof of the consistency of the nonexistence of an isomorphic embedding of C({[}0, c]) into a{''}{''}(a)/c (0). (AU) | |
| FAPESP's process: | 06/02378-7 - Infinite Dimensional Analysis |
| Grantee: | Jorge Tulio Mujica Ascui |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 07/08213-2 - Combinatorial aspects of nonseparable Banach spaces structure |
| Grantee: | Christina Brech |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |