LOCALLY BOUNDED NONCONTINUOUS LINEAR-FORMS ON STRONG DUALS OF NONDISTINGUISHED KOTHE ECHELON SPACES

In this note it is proved that if Al (A) is any nondistinguished Kothe echelon space of order one and K. ,0 (AI (A))' is its strong dual, then there is even a linear form : K - C which is locally bounded (i.e. bounded on the bounded sets) but not continuous. It is also shown that every nondistinguished Kothe echelon space contains a sectional subspace with a particular structure