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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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: 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 $E$.


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Additional Information

Si-Kit Chung
Affiliation: Department of Mathematics, University of Hong Kong, Hong Kong
Email: schung@submaths.hku.hk

Denny Leung
Affiliation: Department of Mathematics, National University of Singapore, Singapore 119260, Singapore
Email: matlhh@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05336-8
PII: S 0002-9939(99)05336-8
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