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Weak and unbounded order convergence in Banach lattices

Published online by Cambridge University Press:  09 April 2009

A. W. Wickstead
A. W. Wickstead
Affiliation:
Department of Pure Mathematics, The Queen's University of Belfast.
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Abstract

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A net (xy) in a vector lattice is unbounded order convergent (uo-convergent) to 0 if u ∧ |xv| order converges to 0 for all u ≧ 0. We consider, in a Banach lattice, the relationship between weak and uo-convergence. We characterise those Banach lattices in which weak convergence implies uo-convergence and those in which uo-convergence of a bounded net implies weak convergence. Finally we combine the results to characterise those Banach lattices in which weak and uo-convergence coincide for bounded nets.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 312 - 319
Copyright
Copyright © Australian Mathematical Society 1977

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