Uo-convergence and its applications to Cesàro means in Banach lattices

Niushan Gao, Vladimir G. Troitsky, Foivos Xanthos

A net $(x_{\alpha })$ in a vector lattice $X$ is said to uo-converge to $x$ if $|x_{\alpha }-x|\wedge u\stackrel{\mathrm{o}}{\to }0$ for every $u\ge 0$. In the first part of this paper, we study some func…