Closed ideals in Dirichlet spaces (Q686121)

The author gives a characterization of all closed ideals of a regular Dirichlet space as the subsets of functions in the domain of the Dirichlet form which vanish quasi everywhere outside some measurable set. Moreover he describes the closed ideals in Sobolev spaces \(W_{1,p}\), \(1\leq p<\infty\), in a similar way and gives some applications of these results.