DieudonnéSchwartz theorem in inductive limits of metrizable spaces. II
Author:
Jing Hui Qiu
Journal:
Proc. Amer. Math. Soc. 108 (1990), 171175
MSC:
Primary 46A05
MathSciNet review:
994779
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Abstract: The DieudonnéSchwartz Theorem for bounded sets in strict inductive limits does not hold for general inductive limits . It does if all the are Fréchet spaces and for any there is such that for all . A counterexample shows that this condition is not necessary. When is a strict inductive limit of metrizable spaces , this condition is equivalent to the condition that each bounded set in is contained and bounded in some . Also, some interesting results for bounded sets in inductive limits of Fréchet spaces are given.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199009947791
PII:
S 00029939(1990)09947791
Keywords:
Locally convex spaces,
(strict) inductive limit,
bounded set
Article copyright:
© Copyright 1990
American Mathematical Society
