@incollection{AST_1977__50__151_0, author = {Krengel, Ulrich}, title = {Recent progress on ergodic theorems}, booktitle = {Syst\`emes dynamiques II - Varsovie}, series = {Ast\'erisque}, pages = {151--192}, publisher = {Soci\'et\'e math\'ematique de France}, number = {50}, year = {1977}, mrnumber = {486418}, zbl = {0376.28016}, language = {en}, url = {https://www.numdam.org/item/AST_1977__50__151_0/} }
TY - CHAP AU - Krengel, Ulrich TI - Recent progress on ergodic theorems BT - Systèmes dynamiques II - Varsovie AU - Collectif T3 - Astérisque PY - 1977 SP - 151 EP - 192 IS - 50 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_1977__50__151_0/ LA - en ID - AST_1977__50__151_0 ER -
Krengel, Ulrich. Recent progress on ergodic theorems, dans Systèmes dynamiques II - Varsovie, Astérisque, no. 50 (1977), pp. 151-192. https://www.numdam.org/item/AST_1977__50__151_0/
1. On the ergodic theory of non-integrable functions and infinite measure spaces. Preprint, 1976. | MR | Zbl
:2. Divergence of ergodic ratios for positive Lp-contractions. Preprint.
:
3. Positive Contractions on
4. A pointwise ergodic theorem for
5. A local ratio theorem. Can. J. Math. 22, 545-552, 1970. | DOI | MR | Zbl
and6. A counter example to the Blum-Hanson theorem in general spaces. Pacific J. Math. 50, 305-308, 1974. | DOI | MR | Zbl
, and :7. Convergence of averages of point-transformations. Proc. Amer. Math. Soc. 49, 265-266, 1975. | MR | Zbl
and :8. Weak convergence of positive contractions implies strong convergence of averages. ZW. 32, 139-145, 1975. | DOI | MR | Zbl
and :
9. Remarks on Dilations in
10. On Convergence of Itérâtes of Positive Contractions in
11. Dilations of positive contractions on
12. On positive dilations to isometries in
13. On weak and strong convergence of positive contractions in
14. On operator convergence in Hilbert space and in Lebesgue space. Periodica Math. Hungarica 2, 235-244, 1972. | DOI | MR | Zbl
and :
15. A local ergodic theorem on
16. Extension of the Birkhoff and von Neumann ergodic theorems to semigroup actions. Ann. Inst. Henri Poincaré 7, # 4, 283-291, 1971. | EuDML | Numdam | MR | Zbl
:
17. On the individual ergodic theorem for
18. Sur les sommes d'iteres d'un opérateur positif. In : Théorie Ergodique, Rennes 1973/74. Springer Lecture Notes in Math. 532, 19-34, 1976. | DOI | MR | Zbl
:19. Chaînes abstraites de Markov vérifiant une condition de Orey. ZW 19, 323-329, 1971. | DOI | MR | Zbl
:
20. Théorème ergodique ponctuel pour un semigroupe commutatif finiment engendré de contractions de
21. New conditions for existence of invariant measures in ergodic theory. Proc. Conf. Ergodic Theory, Ohio State Univ. 1970 ; Springer Lecture Notes in Math. 160, 7-17, 1970. | MR | Zbl
:22. Ergodic theorems for operator sequences. ZW 12, 231-240, 1969. | DOI | MR | Zbl
and :23. Un critère probabiliste de compacité des groupes. Ann. Prob. 2, No.4, 745-746, 1974. | DOI | MR | Zbl
and :24. Quelques applications probabilistes de la quasi-compacité. AIHP 10, # 3, 301-337, 1974. | EuDML | Numdam | MR | Zbl
and :25. Semi-Gaussian subspaces. Trans. Amer. Math. Soc. 104, 123-131, 1962. | DOI | MR | Zbl
:26. Succesive conditional expectations of an integrable function. Ann. Math. Stat. 33, 887-893, 1962. | DOI | MR | Zbl
:27. The mean ergodic theorem and saturation. Indiana Univ. Math. J. 20, # 12, 1163-1174, 1971. | DOI | MR | Zbl
and :28. An ergodic theorem for operators satisfying norm conditions. J. Math. Mech. 11, 165-172, 1962. | MR | Zbl
:29. A class of linear transformations. Proc. AMS 15, 560-564, 1964. | DOI | MR | Zbl
:30. Linear modulus of a linear operator. PAMS 15, 553-559. | MR | Zbl
and :31. Applications des proprietés de moyenne d'un groupe localement compact à la théorie ergodique. Thèse Univ. Paris VI, 1972.
:32. Applications des propriétés de moyenne d'un groupe localement compact à la théorie ergodique. AIHP 6, # 4, 307-326, 1970. | EuDML | Numdam | MR | Zbl
:Applications des propriétés de moyenne d'un groupe localement compact à la théorie ergodiqueErratum : AIHP 7, # 1, p. 81, 1971. | Zbl
:33. Sur une généralization du théorème de Birkhoff. C.R.Acad. Sci. Paris t. 275, 20 Nov 1972, 1135-1138. | MR | Zbl
:34. Some complements to ergodic theorems for vector-valued functions. Bolletino U.M.I. (5) 13-A, 677-686, 1976. | MR | Zbl
and :35. Convergence des moyennes ergodiques pour des sous-suites. Bull. Soc. math.France 35, 7-15, 1973. | EuDML | Numdam | MR | Zbl
:36. Non cummutative ergodic theorems. Bull. Amer.Math. Soc., to appear 1977. | MR | Zbl
and :37. An individual ergodic theorem for positive operators. Rev. Roumaine Math. Pures Appl. 11, 581-594, 1966. | MR | Zbl
and :38. On the integrability of the supremum of ergodic ratios. Ann. Prob. 1, # 2, 338-340, 1973. | DOI | MR | Zbl
:39. Sur le théorème ergodique sous-additif. C.R. Acad. Sc. Paris, t. 281, 3 déc. 1975, Sér. A., 985-988. | MR | Zbl
:40. Lois "zero ou deux" pour les processus de Markov-applications aux marches aleatoires. AIHP 12, 111-130, 1976. | EuDML | Numdam | MR | Zbl
:41. On invariant measures and ergodic theorems for positive operators. J. Functional Anal. 13, # 3, 252-267, 1973. | DOI | MR | Zbl
and :42. Ein Überblick über einige neuere Ansätze zu den Gesetzen der groben Zahlen. Proc. 4th Conf. Probab. Theory, Brasov, 1971. | Zbl
:43. The pointwise ergodic theorem for amenable groups. Amer. J. Math. 472-487, 1974. | DOI | MR | Zbl
:44. Notwendige und hinreichende Ungleichungen fur die Existenz spezieller L1-Kontraktionen. ZW 33, 317-329, 1976. | DOI | MR | Zbl
:45. On finite invariant measures for Markov operators. PAMS 38, 553-557, 1973. | DOI | MR | Zbl
:46. Ergodic theory of Markov processes. van Nostrand Math. Studies # 21, van Nostrand, New York, 1969. | MR | Zbl
:47. On the "zero-two" law. Israel J. Math. 10, 275-280, 1971. | DOI | MR | Zbl
:48. More on the "zero-two" law, preprint. | MR | Zbl
:49. Convergence of the iterates of an operator. Israël J.Math. 16, 159-161, 1973. | DOI | MR | Zbl
:50. Some ratio limit theorems for Markov operators. ZW 23, 55-66, 1972. | DOI | MR | Zbl
and :51. On convex power series of a conservative Markov operator. PAMS 38, 325-330, 1973. | DOI | MR | Zbl
and :52.On invariant functions for positive operators. Colloq. Math. 22, 75-84, 1970. | DOI | EuDML | MR | Zbl
:53. Weak convergence of semigroups implies strong convergence of weighted averages. PAMS 56, 157-161, 1976. | DOI | MR | Zbl
:54. On the convergence of ergodic ratios for positive operators, preprint. | MR | Zbl
and :55. On unaveraged convergence of positive operators in Lebesgue space. TAMS 178, 1-15, 1973. | MR | Zbl
and :
56. On a mixing property of operators in
57. On the ratio ergodic theorem for semigroups. Pacif. J. Math. 39, # 3, 659-667, 1971. | DOI | MR | Zbl
and :58. Ergodic behaviour of diagonal measures and a theorem of Szemerédi on arithmetic progressions. I, II, III. | Zbl
:59. A remark on Chacun's ergodic theorem. Rev. Roum. Math. Pures et Appl. 21, # 5, 521-522, 1976. | MR | Zbl
:60. Weakly wandering vectors for compactly generated groups of unitary operators. J. Math. Anal. Appl. 46, 565-594, 1974. | DOI | MR | Zbl
:61. On finite équivalent invariant measures for semigroups of transformations. Duke Math. J. 38, # 2,395-408, 1971. | MR | Zbl
:62. A local ergodic theorem in Lebesgue space.
:
63. A pointwise Abelian ergodic theorem for
64. On almost everywhere convergence of Abel means of contraction semigroups. Pacific J. Math. 65, 2, 405-408, 1976. | DOI | MR | Zbl
:65. On the local ergodic theorems of Krengel, Kubokawa, and Terrell. Commentationes Math. Univ. Carolinae, 17, 1, 49-59, 1976. | EuDML | MR | Zbl
:66. Ergodic theorems and the construction of summing séquences in amenable locally compact groups. Comm. Pure and Appl. Math. 26, 29-46, 1973. | DOI | MR | Zbl
:67. On matrix summation and the pointwise ergodic theorem. In : Théorie Ergodique Rennes 1973/74 ; Springer Lecture Notes in Math. 532, 113-124, 1976. | DOI | MR | Zbl
and :68. Postulâtes for subadditive processes. Ann. Probab. 2, # 4, 652-680, 1974. | DOI | MR | Zbl
:69. Vector valued ergodic theorems for a 1-parameter semigroup of linear operators. Preprint. | DOI | MR | Zbl
, and :
70. Transition probabilities and contractions of
71. Semigroups of Markov operators. AIHP, B (N.S.) 10, 155-166, 1974. | EuDML | Numdam | MR | Zbl
:
72. Ergodic properties of isometries in
73. An
74. Ergodic properties of semi-Markovian operators on the
75. Theorems for conditional expectations with applications to Markov processes. Israel J. Math16, 362-374, 1973. | DOI | MR | Zbl
:76. A central limit theorem for the subadditive process and its applications to products of random matrices. To appear in : Publ. RIMS, Kyoto Univ. | MR | Zbl
:77. On a class of operators and ergodic theory I. Rev. Roum. Math. Pures et Appl. 19, No.4, 411-420, 1974. | MR | Zbl
:78. On a class of operators and ergodic theory II, preprint. | MR | Zbl
:79. Some remarks on a class of semi-groups of operators I. ZW 26, 241-243, 1973. | MR | Zbl
:80. Neuere Methoden und Ergebnisse der Ergoden-theorie. Ergebn.d.Math. N.F. Heft 29, Springer, Berlin-Göttingen-Heidelberg, 1960. | MR | Zbl
:81. Lecture Notes on Ergodic Theory, Aarhus Univ., Matematisk Inst., 1962-63. | MR | Zbl
:82. A mean ergodic theorem for weakly mixing operators. Adv. in Math. 7, 211-216, 1971. | DOI | MR | Zbl
:83. An elementary lemma on séquences of integers and its applications to functional analysis. Math. Z. 126, 299-307, 1972. | DOI | EuDML | MR | Zbl
:84. A Generalization of the Mean Ergodic Theorem in Banach Spaces. ZW 27, 105-107, 1973. | DOI | MR | Zbl
:85. A note on the Blum-Hanson theorem. PAMS 30, #1, 202-203, 1971. | MR | Zbl
and :86. Ergodic theorems of weak mixing type. PAMS 57, #1, 50-52, 1976. | DOI | MR | Zbl
and :87. Unimodular eigenvalues and weak mixing, preprint. | MR | Zbl
and :88. On the decomposition of a subadditive process. Ann. Prob. 5, #2, 298-302, 1977. | DOI | MR | Zbl
:89. Dilations of positive operators : Construction and Ergodic Theory. Preprint. | MR
, and :90. The General Random Ergodic Theorem I, II. ZW 22, 120-135 u. 136-144, 1972. | DOI | MR | Zbl
:91. Subadditive ergodic theory. Ann. Prob. 1, 883-909, 1973. | DOI | MR | Zbl
:92. The ergodic theory of subadditive stochastic processes. J. Roy. Statist. Soc. B 30, 499-510, 1968. | MR | Zbl
:
93. Majoration des semi-groupes de contractions de
94. Abelian ergodic theorems for vector valued functions. Glasgow Math. Journ., 16, 57-60, 1975. | DOI | MR | Zbl
:95. On the global limit behaviour of Markov chains and of general nonsingular Markov processes. ZW 6, 4, 302-316, 1966. | DOI | MR | Zbl
:96. A necessary and sufficient condition for the validity of the local ergodic theorem. Springer Lecture Notes in Math. 89, 170-177, 1969. | MR | Zbl
:97. A local ergodic theorem. Invent. math. 6, 329-333, 1969. | DOI | EuDML | MR | Zbl
:98. On the individual ergodic theorem for subsequences. Ann. Math. Stat. 42, 1091-1095, 1971. | DOI | MR | Zbl
:99. Weakly wandering vectors and weakly independent partitions. TAMS 164, 199-226, 1972. | DOI | MR | Zbl
:100. Un théorème ergodique pour les processus sur-stationnaires. C.R. Acad.Sci. Paris, t. 282 (3 mai 1976), Sér.A. 1019-1021. | MR | Zbl
:
101. A local ergodic theorem for semigroups in
102. A pointwise ergodic theorem for positive bounded operators. Proc. Jap. Acad. 48, # 7, 458-460, 1972. | DOI | MR | Zbl
:103. A general local ergodic theorem. Proc. Jap. Acad. 48, #7, 461-465, 1972. | DOI | MR | Zbl
:104. Ergodic theorems for contraction semigroups. J. Math. Soc. Japan, 27, 2, 184-193, 1975. | DOI | MR | Zbl
:105. Mixing for Markov operators. ZW 19, 231-242, 1971. | DOI | MR | Zbl
:106. Semi-groups of Markov operators. Bolletino U.M.I. 6, 20-44, 1972. | MR | Zbl
:107.Strong ratio limit theorems for Markov processes. Ann. Math. Stat. 43, #2, 569-579, 1972. | DOI | MR | Zbl
:108. On the uniform ergodic theorem. PAMS 43, #2, 337-340, 1974. | DOI | MR | Zbl
:109. On the uniform ergodic theorem II. PAMS 46, #1, 1-9, 1974. | MR | Zbl
:110. Convergence of the iterates of a Markov operator. ZW, 29, 153-163, 1974. | DOI | MR | Zbl
:111. Quasi-compactness and uniform ergodicity of Markov operators. AIHP, B (N.S.) 11, # 4, 345-354, 1975/76. | EuDML | Numdam | MR | Zbl
:112. On quasi-compact Markov operators. Ann.Prob. 2, 464-475, 1974. | DOI | MR | Zbl
:113. Unaveraged convergence of the iterates of a Markov operator. Preprint. | MR | Zbl
:114. Operator representations of compact groups and ergodic theorems of weak-mixing type. Preprint.
:115. On the mean ergodic theorem of Sine. PAMS 56, 121-126, 1976. | DOI | MR | Zbl
:116. Théorèmes limite quotient pour chaînes de Markov récurrentes au sens de Harris. AIHP, B, 8, 93-105, 1972. | EuDML | Numdam | MR | Zbl
:117. Ergodic and Mixing Properties of Linear Operators. Proc. Royal Irish Acad. 74, 245-261, 1974. | MR | Zbl
:118. Existence of bounded invariant measures in ergodic theory. Symp. 5th Berkeley Symp. Math.Stat. Prob. II (2) 461-472, 1967. | MR | Zbl
:119. Potentiels Markoviens récurrents des chaînes de Harris. Ann.Inst.Fourier 22, #2, 85-130, 1972. | DOI | EuDML | Numdam | MR | Zbl
:120. A constructive ergodic theorem. TAMS 164, 115-137, 1972. | DOI | MR | Zbl
:A constructive ergodic theorem. Erratum TAMS 216, 393, 1976. | Zbl
:121. The sums of iterates of a positive operator. Advances in Prob. 2, 85-115, 1970. | MR | Zbl
:122. A remark on the Birkhoff ergodic theorem. Illin. J. Math. 15, 77-79, 1971. | MR | Zbl
:
123. An operator theorem on
124. A martingale approach to the convergence of the iterates of a transition function. Preprint. | DOI | MR | Zbl
:125. On the individual ergodic theorem for subsequences. Preprint. | MR | Zbl
:126. General ergodic theorems for locally compact groups. Amer. Journ. Math. 63, #1, 1971. | MR | Zbl
:127. Markov Chains. North Holland Math.Library Vol. 11, North Holland/American Elsevier. Amsterdam, Oxford, New York 1975. | MR | Zbl
:128. Markoff-Ketten bei sich fiillenden Löchern im Zustandsraum. Ann. Inst. Fourier, Grenoble 21 (1), 253-270, 1971. | DOI | EuDML | Numdam | MR | Zbl
:
129. Charakterisierung einer Ordnung von konischen Maßen durch positive
130. Topics in ergodic theory. Prob.Winter School (Proc. IVth Winter School Karpacz 1975), Springer Lecture Notes in Math. 472, 131-156. | DOI | MR | Zbl
:131. On finite invariant measures for semi-groups of operators. Canad. Math. Bull., 14, (2), 1971. | MR | Zbl
:
132. Ergodic theorems for semigroups in
133. On a local ergodic theorem. Studia Math. 58, 1-5, 1976. | DOI | EuDML | MR | Zbl
:134. A note on a local ergodic theorem. Comment. Math. Univ.Carolinae, 16, #1, 1-11, 1975. | EuDML | MR | Zbl
:135. Finite invariant measures in ergodic theory. Preprint 1973.
:136. A mean ergodic theorem for a contraction semigroup in Lebesgue space. Studia Math. 54, # 3, 213-219, 1975/76. | DOI | EuDML | MR | Zbl
:137.Reduction of a Sub-Markov operator to its irreducible components. Nat.Sci.Rep. of Ochakomizu Univ. 24, 35-59, 1973. | MR | Zbl
and :138. A mean ergodic theorem. PAMS 24/438-439, 1970. | DOI | MR | Zbl
:139. On the existence of probability measures with given marginals. Ann.Math.Statist. 36, 423-439, 1965. | DOI | MR | Zbl
:140. Problems. Probability in Banach Spaces, Oberwolfach 1975, Springer Lecture Notes in Math. 526, 285-290, 1976. | Zbl
:141. Weakly wandering vectors for representations of groups with precompact conjugacy classes. Preprint.
:142. Ergodic theory for general dynamic Systems. Soviet Math.Doklady 8, # 5, 1213-1216, 1967. | Zbl
:143. Local ergodic theorems for N-parameter semigroups of operators. Lecture Notes in Math. 160, Springer, Berlin-Heidelberg-New York, 1970. | Zbl
:144. The local ergodic theorem and semigroups of non-positive operators. J. Funct. Anal. 10, 424-429, 1972. | DOI | MR | Zbl
:145. A simple proof of the maximal ergodic theorem. Canad. J. Math. 28, # 5, 1073-1075, 1976. | DOI | MR | Zbl
:146. An ergodic theorem for a semigroup of linear contractions. Proc. Jap. Acad. 49, # 5, 306-309, 1973. | DOI | MR | Zbl
:147. On random ergodic theorems for a random quasi-semigroup of linear contractions. Proc.Japan Acad. 48, # 3, 149-152, 1972. | DOI | MR | Zbl
:148. Ergodic theorems for vector valued functions. Preprint.
:149. Multiparameter subadditive processes. Ann.Prob. 4, 772-782, 1976 | DOI | MR | Zbl
:150. Ergodic theorems for convex sets and operator algebras. Invent. math. 37, 201-214, 1976. | DOI | EuDML | MR | Zbl
:151. Ergodic theorems for general dynamical Systems. Trudy Moskov. Mat Obsc. 26, 1972. | MR | Zbl
:Ergodic theorems for general dynamical Systems. Translation in : Trans. Moscow Math. Soc. 26, 94-132, 1972. | Zbl
:152. Ergodic theorems for spatial processes. Preprint, Bielefeld, 1977. | MR | Zbl
and :153. Ergodic theorems for subadditive spatial processes. Preprint, Bielefeld, 1977. | MR
:154. Inequalities for the ergodic maximal function. Studia Math. T. LX., 111-129, 1977. | DOI | EuDML | MR | Zbl
:155. The ergodic maximal function with cancellation. Ann.Prob. 4, 91-97, 1976. | DOI | MR | Zbl
:156. The converse of the dominated ergodic theorem. Preprint. | DOI | MR | Zbl
: