We give a complete description of those relatively uniformly vector lattices \(A\) with the property that every orthomorphism on \(A\) is in the ideal center of \(A\), which gives a positive answer to a problem raised in Wickstead (Compos Math 35(3):225–238, 1977). The idea comes from Basly and Triki (On uniformly closed ideals in f-algebras, In: 2nd Conference, functions spaces. Marcel Dekker 29–33, 1995).
KeywordsCenter of a vector lattice Hyper-Archimedean vector lattice Orthomorphism
Mathematics Subject Classification (2000)Primary 46B42 47B65
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