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.
|Number of pages||4|
|Journal||International Journal of Mathematics and Mathematical Sciences|
|State||Published - 1989|
- Locally barreled space
- bounded set for 5-topology