On the Perturbation of Isometric Groups

LetAbe the infinitesimal generator of an isometric group on a Hilbert spaceHandBbe the perturbed operator ofA. Assume thatBis dissymmetrical and its relative boundary aboutAis smaller than one. Using perturbation theorems ofm-dissipative operation and self-adjoint operators, itwas proved thatA +Bis also an infinitesimal generator of the isometric group. An example of Schr dinger equation with initial value problemwas presented to illustrate the obtained results.