Locally bounded noncontinuous linear forms on strong duals of nondistinguished Köthe echelon spaces. (English) Zbl 0724.46006

Bastin, Françoise; Bonet, José

Proc. Am. Math. Soc. 108, No. 3, 769-774 (1990).

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.

Reviewer: W.Roelcke (München)

MSC:

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

Keywords:

nondistinguished Köthe echelon space