Abstract We give necessary and sufficient conditions for a regular semi-Dirichlet form to enjoy new Feller type property, which we call weak property . Our characterization involves potential theoretic as well probabilistic aspects seems be even in the symmetric case. As consequence, case, obtain variant of decomposition principle essential spectrum (the self-adjoint operators induced by) Diric...

Consider the discrete Laplacian operator A acting on l2(Z). It is well known from classical literature that essential spectrum of a compact interval. In this article, we give an elementary proof for result, using finite-dimensional truncations An A. We do not rely symbol analysis or any infinite-dimensional arguments. Instead, consider eigenvalue-sequences and make use filtration techniques due...