The variational approach to the Dirichlet problem in C*-algebras
Volume 43 / 1998
Banach Center Publications 43 (1998), 135-146
DOI: 10.4064/-43-1-135-146
Abstract
The aim of this work is to develop the variational approach to the Dirichlet problem for generators of sub-Markovian semigroups on C*-algebras. KMS symmetry and the KMS condition allow the introduction of the notion of weak solution of the Dirichlet problem. We will then show that a unique weak solution always exists and that a generalized maximum principle holds true.
