Two problems posed by Choquet and Foias are solved:
(i) Let be a positive linear operator on the space of continuous real-valued functions on a compact Hausdorff space . It is shown that if converges pointwise to a continuous limit, then the convergence is uniform on .
(ii) An example is given of a Choquet simplex and a positive linear operator on the space of continuous affine real-valued functions on , such that
for each in , but does not converge to 0.
On résoud deux problèmes posés par Choquet et Foias:
(i) Soit un opérateur linéaire positif sur l’espace des fonctions réelles continues sur un espace compact . On montre que si la suite des moyennes converge vers une fonction continue, la convergence est uniforme.
(ii) On donne un exemple de simplexe de Choquet et d’un opérateur linéaire positif sur l’espace des fonctions réelles affines continues sur , telles que
pour tout de , bien que ne converge pas vers 0.
@article{AIF_1978__28_3_209_0, author = {Batty, Charles J. K.}, title = {On some ergodic properties for continuous and affine functions}, journal = {Annales de l'Institut Fourier}, pages = {209--215}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {28}, number = {3}, year = {1978}, doi = {10.5802/aif.710}, zbl = {0352.47003}, mrnumber = {80e:47007}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.710/} }
TY - JOUR AU - Batty, Charles J. K. TI - On some ergodic properties for continuous and affine functions JO - Annales de l'Institut Fourier PY - 1978 SP - 209 EP - 215 VL - 28 IS - 3 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.710/ DO - 10.5802/aif.710 LA - en ID - AIF_1978__28_3_209_0 ER -
%0 Journal Article %A Batty, Charles J. K. %T On some ergodic properties for continuous and affine functions %J Annales de l'Institut Fourier %D 1978 %P 209-215 %V 28 %N 3 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.710/ %R 10.5802/aif.710 %G en %F AIF_1978__28_3_209_0
Batty, Charles J. K. On some ergodic properties for continuous and affine functions. Annales de l'Institut Fourier, Volume 28 (1978) no. 3, pp. 209-215. doi : 10.5802/aif.710. https://aif.centre-mersenne.org/articles/10.5802/aif.710/
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