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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Copies of $c_{0}$ and $\ell _{\infty }$
in topological Riesz spaces


Authors: Lech Drewnowski and Iwo Labuda
Journal: Trans. Amer. Math. Soc. 350 (1998), 3555-3570
MSC (1991): Primary 46A40, 46E30, 46B42, 28B05, 40A99
MathSciNet review: 1466947
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Abstract: The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of $c_{0}$ or $\ell _{\infty }$.


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Additional Information

Lech Drewnowski
Affiliation: Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60–769 Poznań, Poland
Email: drewlech@math.amu.edu.pl

Iwo Labuda
Affiliation: Department of Mathematics, University of Mississippi, University, Missouri 38677
Email: mmlabuda@vm.cc.olemiss.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02157-6
PII: S 0002-9947(98)02157-6
Keywords: Topological Riesz space, space of measurable functions, Lebesgue property, Levi property, Orlicz-Pettis theorem, copy of $c_{0}$, copy of $\ell _{\infty }$
Received by editor(s): September 9, 1996
Additional Notes: The paper was written while the first author held a visiting position in the Department of Mathematics, University of Mississippi, in the Spring and Fall Semesters of 1996. He was also partially supported by the State Committee for Scientific Research (Poland), grant no 2 P301 003 07.
Article copyright: © Copyright 1998 American Mathematical Society