On order continuous norms
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- by Si-Kit Chung and Denny Leung PDF
- Proc. Amer. Math. Soc. 128 (2000), 1971-1974 Request permission
Abstract:
It is shown that a normed vector lattice $(E,\Vert \cdot \Vert )$ is order continuous if and only if, for every lattice norm $\rho$ on $E$ with $\rho \leq \Vert \cdot \Vert$, the $\Vert \cdot \Vert$-topology and $\rho$-topology coincide on every order interval of $E$.References
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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
- MR Author ID: 113100
- Email: matlhh@nus.edu.sg
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 1971-1974
- MSC (1991): Primary 46E30
- DOI: https://doi.org/10.1090/S0002-9939-99-05336-8
- MathSciNet review: 1664353