ON THE ESSENTIAL SPECTRUM OF TRANSPORT OPERATORS ON L(1)-SPACES

In a recent article by the first author [J. Math. Phys. 35, 6199-6212 (1994)] the essential spectrum of transport operator was analyzed in L (p)-spaces for p epsilon (1, + infinity). The purpose of the present w ork is to extend this analysis to the case of L(1)-spaces. After estab lishing preliminary results we define the notion of the weak spectrum which we characterize by means of Fredholm operators. We show, in part icular, that in L(1)-spaces the weak spectrum is nothing else but the essential spectrum. Using the same techniques as in the above-mentione d work, we prove the stability of the essential spectrum of a one-dime nsional transport operator with general boundary conditions when an ab stract boundary operator relates the incoming and the outgoing fluxes. Sufficient conditions are given in terms of boundary and collision op erators, assuring the stability of the essential spectrum. We show als o that our results remain valid for neutron transport operators in arb itrary dimension. (C) 1996 American Institute of Physics.