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Norm and order properties of Banach lattices
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1980
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