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A characterization of an order ideal in Riesz spaces

Author(s): S. Alpay; E. Yu. Emel'yanov; Z. Ercan
Journal: Proc. Amer. Math. Soc. 132 (2004), 3627-3628.
MSC (2000): Primary 46A40
Posted: May 12, 2004
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Abstract: In this paper we give a characterization of order ideals in Riesz spaces.

References:

[1]: W.A.J. Luxemburg and A.C. Zaanen, Riesz Spaces I, North-Holland Mathematical Library. North-Holland Publishing Co., Amsterdam-London; New York, 1971. MR 58:23483
[2]: A.C. Zaanen, Ideals in Riesz spaces. Troisième Colloque sur l'Analyse Fonctionnelle (Liège, 1970), pp. 137-146. Vander, Louvain, 1971. MR 53:3640
[3]: A.C. Zaanen, Introduction to operator theory in Riesz spaces, Springer-Verlag, Berlin, 1997. MR 2000c:47074

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Additional Information:

S. Alpay
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: safak@math.metu.edu.tr

E. Yu. Emel'yanov
Affiliation: Sobolev Institute of Mathematics, Acad. Koptyug pr. 4, 630090 Novosibirsk, Russia
Address at time of publication: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: emelanov@math.nsc.ru

Z. Ercan
Affiliation: Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
Email: zercan@metu.edu.tr

DOI: 10.1090/S0002-9939-04-07467-2
PII: S 0002-9939(04)07467-2
Keywords: Riesz spaces, order ideals
Received by editor(s): July 7, 2003
Received by editor(s) in revised form: August 13, 2003
Posted: May 12, 2004
Additional Notes: This work was supported by the Scientific and Technical Research Council of Turkey.
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2004, American Mathematical Society


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