II: 10, 171-174, LNM 51 (1968)
MEYER, Paul-André
Les résolvantes fortement fellériennes d'après Mokobodzki (
Potential theory)
On a compact space, a submarkov kernel $N$ has the strong Feller property if it maps Borel bounded functions into continuous functions, and the stronger Feller property if the mapping $x\rightarrow \epsilon_x N$ is continuous in the norm topology of measures. It is proved that the product of two strong Feller kernels is stronger Feller, and as a consequence if the kernels of are resolvent are strong Feller they are automatically stronger Feller
Comment: This follows from a result on weakly compact operators on continuous functions due to Grothendieck (
Canadian J. Math.,
5, 1953). Mokobodzki's proof is less general (it uses positivity) but very simple. This result is rather useful
Keywords: Resolvents,
Strong Feller propertiesNature: Exposition
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