Mixed topologies on Saks spaces of vector-valued functions
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866913233902764032 |
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| author | Kruse, Karsten |
| author_facet | Kruse, Karsten |
| contents | We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous semigroups. In particular, we are interested if such Saks spaces are complete, semi-Montel, C-sequential or a (strong) Mackey space with respect to the mixed topology. Further, we consider the question whether the mixed and the submixed topology coincide on such Saks spaces and seek for explicit systems of seminorms that generate the mixed topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04681 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Mixed topologies on Saks spaces of vector-valued functions Kruse, Karsten Functional Analysis Primary 46A70, 46E40, Secondary 46E10, 46E15, 47D06, 54D55 We study Saks spaces of functions with values in a normed space and the associated mixed topologies. We are interested in properties of such Saks spaces and mixed topologies which are relevant for applications in the theory of bi-continuous semigroups. In particular, we are interested if such Saks spaces are complete, semi-Montel, C-sequential or a (strong) Mackey space with respect to the mixed topology. Further, we consider the question whether the mixed and the submixed topology coincide on such Saks spaces and seek for explicit systems of seminorms that generate the mixed topology. |
| title | Mixed topologies on Saks spaces of vector-valued functions |
| topic | Functional Analysis Primary 46A70, 46E40, Secondary 46E10, 46E15, 47D06, 54D55 |
| url | https://arxiv.org/abs/2207.04681 |