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!
|
| Summary: | 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. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |