Asymptotically commuting families of operators

Abstract

We study families of symmetric operators (Q_n) with domains given by the range of self-adjoint contraction semigroups (e^−tHn). Assuming the asymptotic commutativity, lim _n [Q_n, e^−tHn]=0, and certain other estimates, we establish the existence and properties of a limiting self-adjoint operatorQ=lim _n Q_n. We apply these results to the study of an elementary supersymmetry algebra.