A representation of operators in L#(<>) which commute with translation by one in terms of L#(0, 1) operator valued functions of <>. In a subsequent study, this representation is used to employ perturbation techniques, heretofore applicable only to operators with compact ret ret resolvents, to nonself adjoint differential operators with periodic coefficients on L#(<>), and to give conditions on the coefficients of these operators which ensure that they be spectral (completely reducible) even though they have continuous spectrum.
