Abstract of a paper by Y. Deng, M. O’Brien, V. G. Troitsky
This is an announcement for the paper “Unbounded Norm Convergence in Banach Lattices” by Y. Deng, M. O’Brien, V. G. Troitsky. Abstract: A net $(x_\alpha)$ in a vector lattice $X$ is unbounded order convergent to $x\in X$ if $|x_\alpha-x|\hat u$ 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 $\||x_\alpha-x|\hat u\|\rightarrow 0$ 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. The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1605.03538
participants (1)
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Bentuo Zheng (bzheng)