Abstract
LetE be a separable Banach space andμ be a probability measure onE. We consider Dirichlet formsε onL 2 (E, m). A special compactificationM Γ ofE is studied in order to give a simple sufficient condition which ensures that the complementM Γ −E has zeroε-capacity. As an application we prove that the classical Dirichlet forms introduced in Albeverio-Röckner [1] satisfy this sufficient condition.
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References
S. Albeverio, M. Röckner. Classical Dirichlet Forms on Topological Vector Spaces—closability and a Caméron-Martin Formula.J. Funct. Anal., 1990, 88: 395–436.
N. Bouleau, F. Hirsch. Propriété d'absolue Continuité dans les espaces de Dirichlet et Applications aux Equations différentielles Stochastiques. Séminaire de Probabilités XX, Lecture Notes in Mathematics, Vol. 1204, Springer-Verlag, Berlin-Heidelberg-New York, 1986.
G. Choquet. Topology. Academic Press, New York, 1966.
M. Fukushima. Dirichlet Forms and Markov Processes. North-Holland, Amsterdam-Oxford-New York, 1980.
T.W. Gamelin. Uniform Algebras. Prentice-Hall, Englewood Cliffs, 1969.
S. Kusuoka. Dirichlet Forms and Diffusion Processes on Banach Space.J. Fac. Science Univ. Tokyo (Sec. 1), 1982, A 29: 79–95.
S. Song. Admissible Vectors and Their Associated Dirichlet Forms.Potential Analysis, 1992, 1: 319–336.
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Song, S. Compactifications of banach spaces and construction of diffusion processes. Acta Mathematicae Applicatae Sinica 10, 225–232 (1994). https://doi.org/10.1007/BF02006854
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DOI: https://doi.org/10.1007/BF02006854