Derivations as square roots of Dirichlet forms

摘要

The aim of this work is to analyze the structure of a tracially symmetric Dirichlet form on a C*-algebra, in terms of a killing weight and a closable derivation taking values in a Hilbert space with a bimodule structure. It is shown that the generator of the associate Markovian semigroup always appears, in a natural way, as the divergence of a closable derivation. Applications are shown to the decomposition of Dirichlet forms and to the construction of differential calculus on metric spaces. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 41]