Compactifications of banach spaces and construction of diffusion processes

LetE be a separable Banach space and be a probability measure onE. We consider Dirichlet forms onL² (E, m). A special compactificationM ofE is studied in order to give a simple sufficient condition which ensures that the complementM –E has zero-capacity. As an application we prove that the classical Dirichlet forms introduced in Albeverio-Röckner [1] satisfy this sufficient condition.