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Locally bounded noncontinuous linear forms on strong duals of nondistinguished Köthe echelon spaces. (English) Zbl 0724.46006
For every nondistinguished Köthe echelon space \(\lambda_ 1(A)\) it is shown that
(i) there exists a linear form on the strong dual of \(\lambda_ 1(A)\) which is locally bounded but not continuous.
(ii) \(\lambda_ 1(A)\) contains a sectional subspace with a structure similar to the original Köthe-Grothendieck example of a nondistinguished Köthe echelon space.

MSC:
46A45 Sequence spaces (including Köthe sequence spaces)
46A04 Locally convex Fréchet spaces and (DF)-spaces
46A08 Barrelled spaces, bornological spaces
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