Some order and topological properties of locally solid linear topological Riesz spaces-Reference-Cited by-同舟云学术

Some order and topological properties of locally solid linear topological Riesz spaces

Published:1973 Issue:2 Volume:40 Page:443-447
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Aliprantis C. D.

Abstract

A theorem of Luxemburg and Zaanen on normed Riesz spaces (Theorem 2.4 below) and one of Nakano (Theorem 2.3 below) have been extended by the author in [1] to metrizable locally solid linear topological Riesz spaces. This note gives an example which shows they cannot be further extended to nonmetrizable Hausdorff locally solid linear topological Riesz spaces.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1973-040-02/S0002-9939-1973-0320692-9/S0002-9939-1973-0320692-9.pdf

Reference6 articles.

1. C. D. Aliprantis, On order and topological properties of Riesz spaces, Thesis, California Institute of Technology, 1973.

2. J. Hornáth, Topological vector spaces and distributions. I, Addison-Wesley, London, 1966.

3. Notes on Banach function spaces. XIVa;Luxemburg, W. A. J.;Nederl. Akad. Wetensch. Proc. Ser. A 68=Indag. Math.,1965

4. Notes on Banach function spaces. IX;Luxemburg, W. A. J.;Nederl. Akad. Wetensch. Proc. Ser. A 67=Indag. Math.,1964

5. \bysame, Riesz spaces. I, North-Holland, Amsterdam, 1971.

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