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On order continuous norms

Authors: Si-Kit Chung and Denny Leung
Journal: Proc. Amer. Math. Soc. 128 (2000), 1971-1974
MSC (1991): Primary 46E30
Published electronically: November 24, 1999
MathSciNet review: 1664353
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Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that a normed vector lattice $(E,\|\cdot\|)$ is order continuous if and only if, for every lattice norm $\rho$ on $E$ with $\rho\leq \|\cdot\|$, the $\|\cdot\|$-topology and $\rho$-topology coincide on every order interval of $E$.

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

  • 1. C. Aliprantis and O. Burkinshaw, Positive Operators, Academic Press, New York and London, 1985. MR 87h:47086
  • 2. J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II, Function Space, Springer-Verlag, Berlin, 1979. MR 81c:46001
  • 3. P. Meyer-Nieberg, Charakterisierung einiger topologischer und ordnungstheoretischer Eigenschaften von Banachverb$\ddot{a}$nden mit Hilfe disjunkter Folgen, Arch. Math., 24 (1973), 640-647. MR 49:5771
  • 4. -, Banach Lattices, Springer-Verlag, New York, 1991. MR 93f:46025
  • 5. H. H. Schaefer, Banach Lattices and Positive Operators, Springer-Verlag, Berlin, 1974. MR 54:11023
  • 6. A. C. Zaanen, Riesz Spaces II, North-Holland, 1983. MR 86b:46001

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Additional Information

Si-Kit Chung
Affiliation: Department of Mathematics, University of Hong Kong, Hong Kong

Denny Leung
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260, Singapore

Keywords: Normed vector lattices, order continuous norms
Received by editor(s): May 4, 1998
Received by editor(s) in revised form: August 13, 1998
Published electronically: November 24, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society

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