Closability of positive symmetric bilinear forms with applications to classical and stable forms on finite and infinite dimensional state spaces
Let \((E, {\mathcal B})\) be a measurable space and \(\mu\) a \(\sigma\)-finite measure on \((E, {\mathcal B})\). Suppose that \(({\mathcal E}, D({\mathcal E}))\) is a closed positive symmetric bilinear form on \(L^2(E, \mu)\). In this paper the author provides conditions that guarantee the closability of the form \({\mathcal E}\) on a different \(L^2\) space \(L^2(E, M)\), where \(M\) is another \(\sigma\)-finite measure on \((E, {\mathcal B})\). The main results of this paper are generalizations of the results by \textit{M. Fukushima}, \textit{K. Sato} and \textit{S. Taniguchi} [Osaka J. Math. 28, 517--535 (1991; Zbl 0756.60071)]. The author also gives applications of the main results to diffusion type forms and their fractional powers corresponding to second quantization.
scientific article; zbMATH DE number 1997247