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WHEN LATTICE HOMOMORPHISMS OF ARCHIMEDEAN VECTOR LATTICES ARE RIESZ HOMOMORPHISMS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 87 / Issue 2 / October 2009
- Published online by Cambridge University Press:
- 09 October 2009, pp. 263-273
- Print publication:
- October 2009
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- Article
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Let A, B be Archimedean vector lattices and let (ui)i∈I, (vi)i∈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
for each λ∈ℝ+ and i∈I, then T is linear. This generalizes earlier results of Ercan and Wickstead (Math. Nachr279 (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).
for each 