Extension of vector-lattice homomorphisms revisited. (English) Zbl 0589.46002

The author provides a new proof to the well-known result: Let X and Y be vector lattices with Y order complete and let M be a majorizing vector sublattice of X. Then every vector-lattice homomorphism \(T: M\to Y\) extends to a vector-lattice homomorphism \(S: X\to Y\). It differs from others [see, for example, W. A. J. Luxemburg and A. R. Schep, Indag. Math. 41, 145-154 (1979; Zbl 0425.46006)] in that the first step of adding one single element does not require Zorn’s lemma.
Reviewer: Lee Peng-Yee


46A22 Theorems of Hahn-Banach type; extension and lifting of functionals and operators
46A40 Ordered topological linear spaces, vector lattices
47B60 Linear operators on ordered spaces


Zbl 0425.46006