Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Locally bounded noncontinuous linear forms on strong duals of nondistinguished Köthe echelon spaces

Authors: Françoise Bastin and José Bonet
Journal: Proc. Amer. Math. Soc. 108 (1990), 769-774
MSC: Primary 46A45; Secondary 46A06, 46A20
MathSciNet review: 1002152
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this note it is proved that if $ {\lambda _1}(A)$ is any nondistinguished Köthe echelon space of order one and $ {K_\infty } \simeq {({\lambda _1}(A))'_b}$ is its strong dual, then there is even a linear form : $ {K_\infty } \to {\mathbf{C}}$ which is locally bounded (i.e. bounded on the bounded sets) but not continuous. It is also shown that every nondistinguished Köthe echelon space contains a sectional subspace with a particular structure.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46A45, 46A06, 46A20

Retrieve articles in all journals with MSC: 46A45, 46A06, 46A20

Additional Information

Keywords: Köthe echelon spaces, Köthe matrices, distinguished spaces, locally bounded linear forms, continuous linear forms
Article copyright: © Copyright 1990 American Mathematical Society