Norm and order properties of banach lattices

Susan E. Bedingfield, Andrew Wirth

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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.

Original languageEnglish
Pages (from-to)331-336
Number of pages6
JournalJournal of the Australian Mathematical Society
Issue number3
Publication statusPublished - 1980
Externally publishedYes

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