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- Title
Unbounded norm convergence in Banach lattices.
- Authors
Deng, Y.; O'Brien, M.; Troitsky, V.
- Abstract
A net $$(x_\alpha )$$ in a vector lattice X is unbounded order convergent to $$x \in X$$ if $$|x_\alpha - x| \wedge u$$ converges to 0 in order for all $$u\in X_+$$ . This convergence has been investigated and applied in several recent papers by Gao et al. It may be viewed as a generalization of almost everywhere convergence to general vector lattices. In this paper, we study a variation of this convergence for Banach lattices. A net $$(x_\alpha )$$ in a Banach lattice X is unbounded norm convergent to x if for all $$u\in X_+$$ . We show that this convergence may be viewed as a generalization of convergence in measure. We also investigate its relationship with other convergences.
- Subjects
STOCHASTIC convergence; BANACH lattices; MATHEMATICAL bounds; BANACH spaces; RIESZ spaces
- Publication
Positivity, 2017, Vol 21, Issue 3, p963
- ISSN
1385-1292
- Publication type
Article
- DOI
10.1007/s11117-016-0446-9