PIMS URegina Distinguished Lecture: Vladimir G. Troitsky

In this talk, we will discuss the theory of Vector and Banach   lattices, as well as some recent developments. In particular, we will discuss order convergence and unbounded order convergence (uo-convergence). In many classical function spaces, uo-convergence agrees with almost everywhere convergence. Thus, uo-convergence may be viewed as a generalization of almost everywhere convergence from function spaces to general vector lattices. This leads to extensions of several classical theorems from function spaces to vector lattice setting. We will also discuss whether uo-convergence is stable under passing to a sublattice.