A note on perturbation of non-symmetric Dirichlet forms by signed smooth measures*

This article discusses the perturbation of a non-symmetric Dirichlet form, (ɛ,D(ɛ))(ɛ,D(ɛ)), by a signed smooth measure μ, where μ = μ1 - μ2 with μ1 and μ2 being smooth measures. It gives a sufficient condition for the perturbed form (ɛμ,D(ɛμ))(ɛμ,D(ɛμ)) (for some α0 ≥ 0) to be a coercive closed form.