On universal Banach spaces of density continuum

Autor(es)

Brech, Christina ^[1] ; Koszmider, Piotr ^{[2, 3]}

Afiliação do(s) autor(es)

^[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

• Tipo de documento: Artigo Científico
• Fonte: Israel Journal of Mathematics; v. 190, n. 1, p. 93-110, AUG 2012.
• Citações Web of Science: 11

Resumo

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)

• Processo FAPESP: 06/02378-7 - Análise em dimensão infinita
• Beneficiário: Jorge Tulio Mujica Ascui
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 07/08213-2 - Aspectos combinatórios da estrutura de espaços de Banach não-separáveis
• Beneficiário: Christina Brech
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado