L p Spectral Independence of Elliptic Operators via Commutator Estimates

Let {T_p:q₁ p q₂} be a family of consistent C₀ semigroups on L^p(), with q₁,q₂ [1,) and open. We show that certain 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 [q₁,q₂.Applications include the case of Petrovskij correct systems with Hölder continuous coefficients, Schrödinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coefficients.