WHEN LATTICE HOMOMORPHISMS OF ARCHIMEDEAN VECTOR LATTICES ARE RIESZ HOMOMORPHISMS

Let A, B be Archimedean vector lattice, and let (u(t))(t is an element of I) . (v(t))(i is an element of I) be maximal orthogonal systems of A and B, respectively In this paper. we prove that if T is a lattice homomorphism from A into B such that T (lambda u(t)) = lambda v(t) for each lambda is an element of R(+) and i is an element of I. then T is linear This generalizes earlier results of Ercan and Wickstead (Math. Nachr 279 (9-10) (2006). 1024-1027). Lochan and Strauss (J. London Math Soc. (2) 25 (1982). 379-384) Mena and Roth (Proc. Amer Math. Soc 71 (1978), 11-12) and Thanh (Ann Univ Sci Budapest Eotvos Sect Math. 34 (1992). 167-171).