Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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



On duals of weakly acyclic $(LF)$-spaces

Authors: Juan Carlos Díaz and Susanne Dierolf
Journal: Proc. Amer. Math. Soc. 125 (1997), 2897-2905
MSC (1991): Primary 46A13, 46A08
MathSciNet review: 1401734
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For countable inductive limits of Fréchet spaces ($(LF)$-spaces) the property of being weakly acyclic in the sense of Palamodov (or, equivalently, having condition $(M_{0})$ in the terminology of Retakh) is useful to avoid some important pathologies and in relation to the problem of well-located subspaces. In this note we consider if weak acyclicity is enough for a $(LF)$-space $E:= \operatorname {ind} E_{n}$ to ensure that its strong dual is canonically homeomorphic to the projective limit of the strong duals of the spaces $E_{n}$. First we give an elementary proof of a known result by Vogt and obtain that the answer to this question is positive if the steps $E_{n}$ are distinguished or weakly sequentially complete. Then we construct a weakly acyclic $(LF)$-space for which the answer is negative.

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

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46A13, 46A08

Retrieve articles in all journals with MSC (1991): 46A13, 46A08

Additional Information

Juan Carlos Díaz
Affiliation: Departamento de Matemáticas, E.T.S.I.A.M., Universidad de Córdoba, 14004 Córdoba, Spain

Susanne Dierolf
Affiliation: FBIV-Mathematik, Universität Trier, D-54286 Trier, Germany

Received by editor(s): October 6, 1995
Received by editor(s) in revised form: April 24, 1996
Additional Notes: The research of the first author was partially supported by the DGICYT/PB94-0441.
Communicated by: Dale E. Alspach
Article copyright: © Copyright 1997 American Mathematical Society