Cone embeddings for vector lattices.- A vector-valued Hahn-Banach theorem.- Bisublinear and subbilinear functionals.- Extension of L1-valued positive operators.- Extension of positive operators in Lp-spaces.- The Korovkin closure for equicontinuous nets of positive operators.- Korovkin theorems for the identity mapping on classical Banach lattices.- Convergence to vector lattice homomorphisms and essential sets.