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Type: Artigo
Title: On universal Banach spaces of density continuum
Author: Brech, Christina
Koszmider, Piotr
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 ℓ∞/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 ℓ∞/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 ℓ∞/c 0
Subject: Espaços de Banach
Country: Israel
Editor: Springer
Rights: Fechado
Identifier DOI: 10.1007/s11856-011-0183-5
Date Issue: 2012
Appears in Collections:IMECC - Artigos e Outros Documentos

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