  We introduce the notions of approximate innerness and central triviality for
endomorphisms on separable von Neumann factors, and we characterize them for
hyperfinite factors by Connes-Takesaki modules of endomorphisms and modular
endomorphisms which are introduced by Izumi. Our result is a generalization of
the corresponding result obtained by Kawahigashi-Sutherland-Takesaki in
automorphism case.
