The problem of central orthomorphisms in a class of [formula omitted]-lattices

Abstract

We prove that if an F-lattice E is locally bounded (i.e., an open ball in E centered at 0 is topologically bounded) then every orthomorphism in E is central: Orth(E)=Z(E). This solves partially a problem raised recently by Chil and Meyer.For the Nakano (non-Banach) F-lattice E=ℓ(pn), 0<pn<1, the above implication becomes an equivalence.We also study the problem of central orthomorphism in the class of (non-Banach) Musielak–Orlicz sequence spaces ℓΦ. We give a sufficient condition on Φ for a non-central orthomorphism on ℓΦ to exist.