Sup-norm-closable bilinear forms and Lagrangians
Abstract
We consider symmetric non-negative definite bilinear forms on algebras of bounded real valued functions and investigate closability with respect to the supremum norm. In particular, any Dirichlet form gives rise to a sup-norm closable bilinear form. Under mild conditions a sup-norm closable bilinear form admits finitely additive energy measures. If, in addition, there exists a (countably additive) energy dominant measure, then a sup-norm closable bilinear form can be turned into a Dirichlet form admitting a carr\'e du champ. Moreover, we can always transfer the bilinear form to an isometrically isomorphic algebra of bounded functions on the Gelfand spectrum, where these measures exist. Our results complement a former closability study of Mokobodzki for the locally compact and separable case.
Cite
@article{arxiv.1407.1301,
title = {Sup-norm-closable bilinear forms and Lagrangians},
author = {Michael Hinz},
journal= {arXiv preprint arXiv:1407.1301},
year = {2014}
}