Unbounded Norm Convergence in Banach Lattices

Y. Deng, M. O'Brien, V. G. Troitsky

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 ha…