Weak Hopf algebras arising from weak matched pairs

This work extends the idea of matched pairs presented by Majid in Majid and Takeuchi in Takeuchi for the context of weak bialgebras and weak Hopf algebras. We introduce, also inspired by partial matched pairs matchedpair, the notion of weak matched pairs and establish conditions for a subspace of the smash product be a weak bialgebra/Hopf algebra. Further, some new examples of (co) actions of weak bialgebras over algebras and some results about integral elements are presented.