Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces
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 (ve...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/184071 |
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| _version_ | 1832553522988580864 |
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| author | Mirna Džamonja |
| author_facet | Mirna Džamonja |
| author_sort | Mirna Džamonja |
| collection | DOAJ |
| description | 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 CL 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. |
| format | Article |
| id | doaj-art-16e68611923b4650b2a3c106e3364408 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-16e68611923b4650b2a3c106e33644082025-02-03T05:53:45ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/184071184071Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach SpacesMirna Džamonja0School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UKWe 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 CL 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.http://dx.doi.org/10.1155/2014/184071 |
| spellingShingle | Mirna Džamonja Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces Abstract and Applied Analysis |
| title | Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces |
| title_full | Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces |
| title_fullStr | Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces |
| title_full_unstemmed | Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces |
| title_short | Isomorphic Universality and the Number of Pairwise Nonisomorphic Models in the Class of Banach Spaces |
| title_sort | isomorphic universality and the number of pairwise nonisomorphic models in the class of banach spaces |
| url | http://dx.doi.org/10.1155/2014/184071 |
| work_keys_str_mv | AT mirnadzamonja isomorphicuniversalityandthenumberofpairwisenonisomorphicmodelsintheclassofbanachspaces |