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(Ω), with q₁, q₂ ∈ [1, ∞) and Ω ⊆ ℝⁿ 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.