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Proceedings of the American Mathematical Society
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
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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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1002152-5
PII: S 0002-9939(1990)1002152-5
Keywords: Köthe echelon spaces, Köthe matrices, distinguished spaces, locally bounded linear forms, continuous linear forms
Article copyright: © Copyright 1990 American Mathematical Society