L-p spectral independence of elliptic operators via commutator estimates

Let {T-p:q(1) less than or equal to p less than or equal to q(2)} be a fami ly of consistent C-0 semigroups on L-p(Omega), with q(1), q(2) is an elemen t of [1,infinity) and Omega subset of or equal to R-n open. We show that ce rtain commutator conditions on T-p and on the resolvent of its generator A( p) ensure the p independence of the spectrum of A(p) for p is an element of [q(1),q(2)]. Applications include the case of Petrovskij correct systems with Holder con tinuous coefficients, Schrodinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex co efficients.