Norm and order properties of banach lattices

Susan E. Bedingfield; Andrew Wirth

doi:10.1017/S1446788700021339

Norm and order properties of banach lattices

Susan E. Bedingfield, Andrew Wirth

Research output: Contribution to journal › Article › Research › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	331-336
Number of pages	6
Journal	Journal of the Australian Mathematical Society
Volume	29
Issue number	3
DOIs	https://doi.org/10.1017/S1446788700021339
Publication status	Published - 1980
Externally published	Yes

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10.1017/S1446788700021339

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Cite this

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title = "Norm and order properties of banach lattices",

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.",

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AB - 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.

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JO - Journal of the Australian Mathematical Society

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