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Norm and order properties of Banach lattices

Published online by Cambridge University Press:  09 April 2009

Susan E. Bedingfield  and
Andrew Wirth
Susan E. Bedingfield
Affiliation:
Department of Mathematics University of MelbourneParkvile, Victoria 3052, Australia
Andrew Wirth
Affiliation:
Prahran College of Advanced EducationPrahran, Victoria 3181, Australia
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Abstract

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The interrelationships between norm convergence and two forms of convergence defined in terms of order, namely order and relative uniform convergence are considered. The implications between conditions such as uniform convexity, uniform strictness, uniform monotonicity and others are proved. In particular it is shown that a σ-order continuous, σ-order complete Banach lattice is order continuous.

1980 Mathematics subject classification (Amer. Math. Soc.): 46 A 40.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 3 , May 1980 , pp. 331 - 336
Copyright
Copyright © Australian Mathematical Society 1980

References

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