Abstract
Let E and F be Hausdorff locally convex spaces, and let £(E, F) denote the space of continuous linear maps from E to F. Suppose that for every subspace N ⊂ E and an absolutely convex set A ⊂ E which is bounded, closed, and absorbing in TV, there is a barrel D ⊂ E such that A = D ∩ N. Then it is shown that the families of weakly and strongly bounded subsets of £(F, F) are identical if and only if E is locally barreled.
| Original language | English |
|---|---|
| Pages (from-to) | 447-450 |
| Number of pages | 4 |
| Journal | International Journal of Mathematics and Mathematical Sciences |
| Volume | 12 |
| Issue number | 3 |
| DOIs | |
| State | Published - 1989 |
Keywords
- Locally barreled space
- S-topology
- bounded set for 5-topology