Contractions on $L_{1}$-spaces
HTML articles powered by AMS MathViewer
- by M. A. Akcoglu and A. Brunel PDF
- Trans. Amer. Math. Soc. 155 (1971), 315-325 Request permission
Abstract:
It is shown that a linear contraction on a complex ${L_1}$-space can be represented in terms of its linear modulus. This result is then used to give a direct proof of Chaconβs general ratio ergodic theorem.References
- M. A. Akcoglu, Pointwise ergodic theorems, Trans. Amer. Math. Soc. 125 (1966), 296β309. MR 230876, DOI 10.1090/S0002-9947-1966-0230876-7
- Antoine Brunel, Sur un lemme ergodique voisin du lemme de E. Hopf, et sur une de ses applications, C. R. Acad. Sci. Paris 256 (1963), 5481β5484 (French). MR 152633
- R. V. Chacon, Identification of the limit of operator averages, J. Math. Mech. 11 (1962), 961β968. MR 0145352
- R. V. Chacon, Operator averages, Bull. Amer. Math. Soc. 68 (1962), 351β353. MR 142718, DOI 10.1090/S0002-9904-1962-10805-2
- R. V. Chacon, Convergence of operator averages, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) Academic Press, New York, 1963, pp.Β 89β120. MR 0160872
- R. V. Chacon and U. Krengel, Linear modulus of linear operator, Proc. Amer. Math. Soc. 15 (1964), 553β559. MR 164244, DOI 10.1090/S0002-9939-1964-0164244-7
- R. V. Chacon and D. S. Ornstein, A general ergodic theorem, Illinois J. Math. 4 (1960), 153β160. MR 110954
- Eberhard Hopf, The general temporally discrete Markoff process, J. Rational Mech. Anal. 3 (1954), 13β45. MR 60181, DOI 10.1512/iumj.1954.3.53002
- Eberhard Hopf, On the ergodic theorem for positive linear operators, J. Reine Angew. Math. 205 (1960/61), 101β106. MR 125937, DOI 10.1515/crll.1960.205.101
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 155 (1971), 315-325
- MSC: Primary 28.70; Secondary 47.00
- DOI: https://doi.org/10.1090/S0002-9947-1971-0276439-0
- MathSciNet review: 0276439