Some remarks about Mackey convergence
In this paper, we examine Mackey convergence with respect to K-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K- convergent sequences that are not Mackey convergent; the...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1995-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171295000846 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832547440699375616 |
|---|---|
| author | Józef Burzyk Thomas E. Gilsdorf |
| author_facet | Józef Burzyk Thomas E. Gilsdorf |
| author_sort | Józef Burzyk |
| collection | DOAJ |
| description | In this paper, we examine Mackey convergence with respect to K-convergence
and bornological (Hausdorff locally convex) spaces. In particular,
we prove that: Mackey convergence and local completeness imply property K;
there are spaces having K- convergent sequences that are not Mackey
convergent; there exists a space satisfying the Mackey convergence condition, is
barrelled, but is not bornological; and if a space satisfies the biackey
convergence condition and every sequentially continuous seminorm is
continuous, then the space is bornological. |
| format | Article |
| id | doaj-art-73a551d33f45475a99cb8c45a8f8587a |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1995-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-73a551d33f45475a99cb8c45a8f8587a2025-02-03T06:44:42ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251995-01-0118465966410.1155/S0161171295000846Some remarks about Mackey convergenceJózef Burzyk0Thomas E. Gilsdorf1Institute of Mathematics, Polish Academy of Science, Wieczorka 8, Katowice 40-013, PolandDepartment of Mathematics, University of North Dakota, Grand Forks, ND 58202-8376, USAIn this paper, we examine Mackey convergence with respect to K-convergence and bornological (Hausdorff locally convex) spaces. In particular, we prove that: Mackey convergence and local completeness imply property K; there are spaces having K- convergent sequences that are not Mackey convergent; there exists a space satisfying the Mackey convergence condition, is barrelled, but is not bornological; and if a space satisfies the biackey convergence condition and every sequentially continuous seminorm is continuous, then the space is bornological.http://dx.doi.org/10.1155/S0161171295000846Mackey convergenceproperty Kbarrelled space bornological space. |
| spellingShingle | Józef Burzyk Thomas E. Gilsdorf Some remarks about Mackey convergence International Journal of Mathematics and Mathematical Sciences Mackey convergence property K barrelled space bornological space. |
| title | Some remarks about Mackey convergence |
| title_full | Some remarks about Mackey convergence |
| title_fullStr | Some remarks about Mackey convergence |
| title_full_unstemmed | Some remarks about Mackey convergence |
| title_short | Some remarks about Mackey convergence |
| title_sort | some remarks about mackey convergence |
| topic | Mackey convergence property K barrelled space bornological space. |
| url | http://dx.doi.org/10.1155/S0161171295000846 |
| work_keys_str_mv | AT jozefburzyk someremarksaboutmackeyconvergence AT thomasegilsdorf someremarksaboutmackeyconvergence |