Unbounded Norm Convergence in Banach Lattices
نویسنده
چکیده
A net (xα) in a vector lattice X is unbounded order convergent to x ∈ X if |xα − x| ∧ u converges to 0 in order for all u ∈ 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 (xα) in a Banach lattice X is unbounded norm convergent to x if ∥
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