: 10, 171-174, LNM 51 (1968)MEYER, Paul-André
Les résolvantes fortement fellériennes d'après Mokobodzki
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 FellerComment:
This follows from a result on weakly compact operators on continuous functions due to Grothendieck (Canadian J. Math.
, 1953). Mokobodzki's proof is less general (it uses positivity) but very simple. This result is rather usefulKeywords: Resolvents
, Strong Feller propertiesNature: Exposition Retrieve article from Numdam