Geodesic
Generalized Limits and Related Asymptotic Formulas
Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 612-627

Voir la notice de l'article provenant de la source Math-Net.Ru

On the basis of the new version of Karamata's theorem, stated in terms of generalized limits, we succeed in weakening the conditions of validity of the Connes asymptotic formulas studied by many authors. Using this approach, we can apply the criterion of “measurability” due to Connes for passing from generalized limits to ordinary limits.
Keywords: generalized limit, Dixmier trace, operator ideal, Cesàro operator, Karamata theorem, Hilbert space, dilation operator.
Mots-clés : Marcinkiewicz space, Lebesgue–Stieltjes integral 
@article{MZM_2009_86_4_a12,
     author = {A. A. Sedaev},
     title = {Generalized {Limits} and {Related} {Asymptotic} {Formulas}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {612--627},
     publisher = {mathdoc},
     volume = {86},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a12/}
}
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A. A. Sedaev. Generalized Limits and Related Asymptotic Formulas. Matematičeskie zametki, Tome 86 (2009) no. 4, pp. 612-627. http://geodesic.mathdoc.fr/item/MZM_2009_86_4_a12/