Completions of Locally Convex Spaces and Almost Periodicity
Marko Kostić
Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia
Received on April 15, 2026
Accepted on May 3, 2026
Communicated by Gaston M. N'Guérékata
| Abstract. In this paper, we consider the completions of locally convex spaces, the completions of metric linear spaces and present several new structural results concerning the (Stepanov) ρ-almost periodic functions with values in locally convex spaces. We formulate and prove the Bochner criterion for the (Stepanov) almost periodic functions with values in non-complete locally convex spaces. | |
| Keywords: | ρ-almost periodic functions, Stepanov ρ-almost periodic functions, locally convex spaces, metric linear spaces, completions. |
| 2010 Mathematics Subject Classification: 42A75, 43A60, 46A03, 46A04, 46A30. | |