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Proceedings of the American Mathematical Society

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



A necessary and sufficient condition for $ w\sp *$-bounded sets to be strongly bounded

Authors: Carlos Bosch and Jan Kucera
Journal: Proc. Amer. Math. Soc. 101 (1987), 453-454
MSC: Primary 46A05
MathSciNet review: 908647
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Abstract: It is known that if a locally convex space $ E$ is quasi-complete then every $ \sigma (E',E)$-bounded set in $ E'$ is $ \beta (E',E)$-bounded. This result cannot be reversed. Here we show that every $ \sigma (E',E)$-bounded set is $ \beta (E',E)$-bounded iff $ E$ is fast complete.

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

  • [1] Marc de Wilde, Closed graph theorems and webbed spaces, Pitman, London, 1978.
  • [2] Helmut H. Schaefer, Topological vector spaces, Springer-Verlag, New York-Berlin, 1971. Third printing corrected; Graduate Texts in Mathematics, Vol. 3. MR 0342978
  • [3] Albert Wilansky, Modern methods in topological vector spaces, McGraw-Hill International Book Co., New York, 1978. MR 518316

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Keywords: Quasi-complete space, fast complete space, $ \sigma (E',E)$-bounded set, $ \beta (E',E)$-bounded set
Article copyright: © Copyright 1987 American Mathematical Society

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