Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces

Mirna Džamonja

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: We develop the framework of natural spaces to study isomorphic embeddings of Banach spaces. We then use it to show that a sufficient failure of the generalized continuum hypothesis implies that the universality number of Banach spaces of a given density under a certain kind of positive embedding (very positive embedding) is high. An example of a very positive embedding is a positive onto embedding between C(K) and C(L) for 0‐dimensional K and L such that the following requirement holds for all h ≠ 0 and f ≥ 0 in C(K): if 0 ≤ Th ≤ Tf, then there are constants a ≠ 0 and b with 0 ≤ a · h + b ≤ f and a · h + b ≠ 0.

Date: 2014
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https://doi.org/10.1155/2014/184071

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:184071

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