Let be a locally compact group, and let be a function norm on such that the space of all locally integrable functions with finite -norm is an invariant solid Banach function space. Consider the space of all functions in of which the right translation is a continuous map from into . Characterizations of the case where is a Riesz ideal of are given in terms of the order-continuity of on certain subspaces of . Throughout the paper, the discussion is carried out in the context of and all the results are formulated for foundation semigroups with identity element; any locally compact group is an example of such a semigroup.
Soit un groupe localement compact, et soit une norme de fonctions (c’est-à-dire ayant la propriété de Riesz) sur , telle que le sous-espace , formé des fonctions localement intégrables de -norme bornée, soit un espace de fonctions de Banach invariant et solide (solide dans l’espace de Riesz ). Considérons l’espace , formé des fonctions dans avec une translation à droite qui est une application continue de dans . On trouvera les caractérisations du cas où est un sous-espace solide (un idéal de Riesz). Ces descriptions sont données à l’aide de la continuité pour l’ordre de la norme sur certains sous-espaces de . La discussion entière se déroule et les résultats sont formulés dans le contexte des semi-groupes fondamentaux ayant un élément neutre. Tout groupe localement compact est un cas spécial d’un tel semi-groupe.
@article{AIF_1982__32_2_67_0, author = {Sleijpen, G\'erard L. G.}, title = {The order structure of the space of measures with continuous translation}, journal = {Annales de l'Institut Fourier}, pages = {67--110}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {32}, number = {2}, year = {1982}, doi = {10.5802/aif.873}, zbl = {0468.43001}, mrnumber = {83k:43005}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.873/} }
TY - JOUR AU - Sleijpen, Gérard L. G. TI - The order structure of the space of measures with continuous translation JO - Annales de l'Institut Fourier PY - 1982 SP - 67 EP - 110 VL - 32 IS - 2 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.873/ DO - 10.5802/aif.873 LA - en ID - AIF_1982__32_2_67_0 ER -
%0 Journal Article %A Sleijpen, Gérard L. G. %T The order structure of the space of measures with continuous translation %J Annales de l'Institut Fourier %D 1982 %P 67-110 %V 32 %N 2 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.873/ %R 10.5802/aif.873 %G en %F AIF_1982__32_2_67_0
Sleijpen, Gérard L. G. The order structure of the space of measures with continuous translation. Annales de l'Institut Fourier, Volume 32 (1982) no. 2, pp. 67-110. doi : 10.5802/aif.873. https://aif.centre-mersenne.org/articles/10.5802/aif.873/
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