The problem of central orthomorphisms in a class of FF-lattices

We prove that if an FF-lattice EE is locally bounded (i.e., an open ball in EE centered at 00 is topologically bounded) then every orthomorphism in EE is central: Orth(E)=Z(E)Orth(E)=Z(E). This solves partially a problem raised recently by Chil and Meyer.For the Nakano (non-Banach) FF-lattice E=ℓ(pn)E=ℓ(pn), 0