Mixed topologies on Saks spaces of vector-valued functions

Publikationstyp
Journal Article
Date Issued
2024-03-15
Sprache
English
Author(s)
Kruse, Karsten  orcid-logo
Mathematik E-10  
TORE-URI
https://hdl.handle.net/11420/46096
Journal
Topology and its Applications  
Volume
345
Article Number
108843
Citation
Topology and its Applications 345: 108843 (2024)
Publisher DOI
10.1016/j.topol.2024.108843
Scopus ID
2-s2.0-85184780108
Publisher
Elsevier
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.
Subjects
C-sequential
Mackey
Mixed topology
Saks space
Tight
DDC Class
510: Mathematics