A general differentiation theorem for superadditive processes

Ryotaro Sato

Colloquium Mathematicae (2000)

  • Volume: 83, Issue: 1, page 125-136
  • ISSN: 0010-1354

Abstract

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Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T= T t : 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.

How to cite

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Sato, Ryotaro. "A general differentiation theorem for superadditive processes." Colloquium Mathematicae 83.1 (2000): 125-136. <http://eudml.org/doc/210767>.

@article{Sato2000,
abstract = {Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=$T_t$: 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.},
author = {Sato, Ryotaro},
journal = {Colloquium Mathematicae},
keywords = {differentiation theorem; superadditive process; absolutely continuous norm; local ergodic theorem; semigroup of positive linear operators; Banach lattice of functions; strongly continuous semigroup; positive linear operators; Doob limit},
language = {eng},
number = {1},
pages = {125-136},
title = {A general differentiation theorem for superadditive processes},
url = {http://eudml.org/doc/210767},
volume = {83},
year = {2000},
}

TY - JOUR
AU - Sato, Ryotaro
TI - A general differentiation theorem for superadditive processes
JO - Colloquium Mathematicae
PY - 2000
VL - 83
IS - 1
SP - 125
EP - 136
AB - Let L be a Banach lattice of real-valued measurable functions on a σ-finite measure space and T=$T_t$: 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.
LA - eng
KW - differentiation theorem; superadditive process; absolutely continuous norm; local ergodic theorem; semigroup of positive linear operators; Banach lattice of functions; strongly continuous semigroup; positive linear operators; Doob limit
UR - http://eudml.org/doc/210767
ER -

References

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  1. [1] M. A. Akcoglu and M. Falkowitz, A general local ergodic theorem in L 1 , Pacific J. Math. 119 (1985), 257-264. 
  2. [2] M. A. Akcoglu and U. Krengel, A differentiation theorem for additive processes, Math. Z. 163 (1978), 199-210. 
  3. [3] M. A. Akcoglu and U. Krengel, A differentiation theorem in L p , ibid. 169 (1979), 31-40. 
  4. [4] R. Emilion, Additive and superadditive local theorems, Ann. Inst. H. Poincaré Probab. Statist. 22 (1986), 19-36. Zbl0594.60030
  5. [5] D. Feyel, Convergence locale des processus sur-abéliens et sur-additifs, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 301-303. Zbl0508.60016
  6. [6] T. Kataoka, R. Sato and H. Suzuki, Differentiation of superadditive processes in L p , Acta Math. Hungar. 49 (1987), 157-162. Zbl0646.47026
  7. [7] U. Krengel, A local ergodic theorem, Invent. Math. 6 (1969), 329-333. Zbl0165.37402
  8. [8] U. Krengel, Ergodic Theorems, de Gruyter, Berlin, 1985. 
  9. [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. Zbl0321.28013
  10. [10] R. Sato, On local ergodic theorems for positive semigroups, Studia Math. 63 (1978), 45-55. Zbl0391.47022
  11. [11] H. Suzuki, On the two decompositions of a measure space by an operator semigroup, Math. J. Okayama Univ. 25 (1983), 87-90. Zbl0537.47021
  12. [12] N. Wiener, The ergodic theorem, Duke Math. J. 5 (1939), 1-18. Zbl0021.23501

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