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

Mirna Džamonja

Abstract and Applied Analysis, 2014, vol. 2014, 1-11

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 and for 0-dimensional and such that the following requirement holds for all and in : if , then there are constants and with and .

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:184071

DOI: 10.1155/2014/184071

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