2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/153601We define and investigate pairings of multiplier Hopf algebras. It is shown that two dually paired regular multiplier Hopf ($*$-)algebras $A$ and $B$ yield a quantum double multiplier Hopf ($*$-)algebra which is again regular. Integrals on $A$ and $B$ induce an integral on the quantum double. The results generalize pairing and quantum double construction from ordinary Hopf algebras to multiplier Hopf algebras.AMS-TeX, 21 pagesQuantum AlgebraFunctional Analysis16W30, 17B37text