Bounded Sets in £(E, F)

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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 languageEnglish
Pages (from-to)447-450
Number of pages4
JournalInternational Journal of Mathematics and Mathematical Sciences
Issue number3
StatePublished - 1989


  • Locally barreled space
  • S-topology
  • bounded set for 5-topology


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