Convergence structures and locally solid topologies on vector lattices of operators

Abstract For vector lattices E and F , where is Dedekind complete supplied with a locally solid topology, we introduce the corresponding absolute strong operator topology on order bounded operators $${\mathscr{L}}_{\mathrm{ob}}(E,F)$$ L ob ( E , F ) from into . Using this, it follows that admits Hausdorff uo-Lebesgue whenever does. each of convergence, unbounded and—when applicable—convergence in there are both uniform convergence structure Of six conceivable inclusions within these three pairs, only one generally valid. On orthomorphisms lattice, however, five valid, sixth valid for nets. The latter condition redundant case sequences orthomorphisms, as consequence boundedness principle establish. We furthermore show that, contrast to general operators, preserve not nets, but well.