A general differentiation theorem for superadditive processes
Sato, Ryotaro
Colloquium Mathematicae, Tome 84/85 (2000), p. 125-136 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=Tt: t < 0 be a strongly continuous semigroup of positive linear operators on the Banach lattice L. Under some suitable norm conditions on L we prove a general differentiation theorem for superadditive processes in L with respect to the semigroup T.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210767 
@article{bwmeta1.element.bwnjournal-article-cmv83i1p125bwm,
     author = {Ryotaro Sato},
     title = {A general differentiation theorem for superadditive processes},
     journal = {Colloquium Mathematicae},
     volume = {84/85},
     year = {2000},
     pages = {125-136},
     zbl = {0965.47008},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p125bwm}
}

Sato, Ryotaro. A general differentiation theorem for superadditive processes. Colloquium Mathematicae, Tome 84/85 (2000) pp. 125-136. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv83i1p125bwm/

[000] [1] M. A. Akcoglu and M. Falkowitz, A general local ergodic theorem in L1, Pacific J. Math. 119 (1985), 257-264.

[001] [2] M. A. Akcoglu and U. Krengel, A differentiation theorem for additive processes, Math. Z. 163 (1978), 199-210.

[002] [3] M. A. Akcoglu and U. Krengel, A differentiation theorem in Lp, ibid. 169 (1979), 31-40.

[003] [4] R. Emilion, Additive and superadditive local theorems, Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), 19-36. | Zbl 0594.60030

[004] [5] D. Feyel, Convergence locale des processus sur-abéliens et sur-additifs, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 301-303. | Zbl 0508.60016

[005] [6] T. Kataoka, R. Sato and H. Suzuki, Differentiation of superadditive processes in Lp, Acta Math. Hungar. 49 (1987), 157-162. | Zbl 0646.47026

[006] [7] U. Krengel, A local ergodic theorem, Invent. Math. 6 (1969), 329-333. | Zbl 0165.37402

[007] [8] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985.

[008] [9] D. S. Ornstein, The sums of iterates of a positive operator, in: Advances in Probability and Related Topics, Vol. 2, Dekker, New York, 1970, 85-115. | Zbl 0321.28013

[009] [10] R. Sato, On local ergodic theorems for positive semigroups, Studia Math. 63 (1978), 45-55. | Zbl 0391.47022

[010] [11] H. Suzuki, On the two decompositions of a measure space by an operator semigroup, Math. J. Okayama Univ. 25 (1983), 87-90. | Zbl 0537.47021

[011] [12] N. Wiener, The ergodic theorem, Duke Math. J. 5 (1939), 1-18. | Zbl 0021.23501