A Radon-Nikodym theorem for nonlinear functionals on Banach lattices

A Radon-Nikodym theorem is established for a class of nonlinear orthogonally additive monotone functionals on Dedekind complete Banach lattices. A functional



S
S



is absolutely continuous with respect to



T
T



if




T
(
f
)
=
0

T(f) =0



implies




S
(
f
)
=
0

S( f)=0



for



f
f



in the domain. It is shown that



S
S



is absolutely continuous with respect to



T
T



implies



S
S



is equal to the composition of an extension of



T
T



with an appropriate generalized orthomorphism. In the special case that



S
S



and



T
T



are linear, the generalized orthomorphism reduces to a multiplication operator consistent with the classical formulation of this theorem.