If L is a Riesz space (lattice
ordered vector space), a Riesz homomorphism of L is an order preserving linear
map which preserves the finite operations “∨” and “∧”. It was shown in
our previous paper [“Homomorphisms of Riesz spaces,” Pacific J. Math.]
that there is a large class α of spaces such that if L belongs to a and φ is a
Riesz homomorphism from L onto an Archimedean Riesz space, then φ
preserves the order limit of sequences. In this paper the list of members of
α is extended. It is further shown that there is a large class β of spaces
with the property that if L belongs to α and φ is a Riesz homomorphism
of L into an Archimedean Riesz space then φ preserves the order limit of
sequences.
