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Non-archimedean Eberlein-mulian theory

Author

Listed:
  • T. Kiyosawa
  • W. H. Schikhof

Abstract

It is shown that, for a large class of non-archimedean normed spaces E , a subset X is weakly compact as soon as f ( X ) is compact for all f ∈ E ′ (Theorem 2.1), a fact that has no analogue in Functional Analysis over the real or complex numbers. As a Corollary we derive a non-archimedean version of the Eberlein-mulian Theorem (2.2 and 2.3, for the classical theorem, see [1], VIII, §2 Theorem and Corollary, page 219).

Suggested Citation

  • T. Kiyosawa & W. H. Schikhof, 1996. "Non-archimedean Eberlein-mulian theory," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 19, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:708102
    DOI: 10.1155/S0161171296000907
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