Strong martingale convergence of generalized conditional expectations on von Neumann algebras
HTML articles powered by AMS MathViewer
- by Fumio Hiai and Makoto Tsukada PDF
- Trans. Amer. Math. Soc. 282 (1984), 791-798 Request permission
Abstract:
Accardi and Cecchini generalized the concept of conditional expectations on von Neumann algebras. In this paper we give some conditions for strong convergence of increasing or decreasing martingales of Accardi and Cecchini’s conditional expectations.References
- Luigi Accardi and Carlo Cecchini, Conditional expectations in von Neumann algebras and a theorem of Takesaki, J. Functional Analysis 45 (1982), no. 2, 245–273. MR 647075, DOI 10.1016/0022-1236(82)90022-2
- Huzihiro Araki, On the equivalence of the KMS condition and the variational principal for quantum lattice systems, Comm. Math. Phys. 38 (1974), 1–10. MR 475531
- Huzihiro Araki and Akitaka Kishimoto, On clustering property, Rep. Math. Phys. 10 (1976), no. 2, 275–281. MR 573229, DOI 10.1016/0034-4877(76)90049-5
- Nghiêm Đặng Ngọc, Pointwise convergence of martingales in von Neumann algebras, Israel J. Math. 34 (1979), no. 4, 273–280 (1980). MR 570886, DOI 10.1007/BF02760608
- Gérard G. Emch, Nonabelian special $K$-flows, J. Functional Analysis 19 (1975), 1–12. MR 0448102, DOI 10.1016/0022-1236(75)90002-6
- Gérard G. Emch, Generalized $K$-flows, Comm. Math. Phys. 49 (1976), no. 3, 191–215. MR 434287
- Uffe Haagerup, The standard form of von Neumann algebras, Math. Scand. 37 (1975), no. 2, 271–283. MR 407615, DOI 10.7146/math.scand.a-11606
- Fumio Hiai, Martingale-type convergence of modular automorphism groups on von Neumann algebras, J. Funct. Anal. 56 (1984), no. 3, 265–278. MR 743841, DOI 10.1016/0022-1236(84)90077-6
- E. Christopher Lance, Martingale convergence in von Neumann algebras, Math. Proc. Cambridge Philos. Soc. 84 (1978), no. 1, 47–56. MR 489568, DOI 10.1017/S0305004100054864
- Şerban Strătilă, Modular theory in operator algebras, Editura Academiei Republicii Socialiste România, Bucharest; Abacus Press, Tunbridge Wells, 1981. Translated from the Romanian by the author. MR 696172
- M. Takesaki, Tomita’s theory of modular Hilbert algebras and its applications, Lecture Notes in Mathematics, Vol. 128, Springer-Verlag, Berlin-New York, 1970. MR 0270168
- Masamichi Takesaki, Conditional expectations in von Neumann algebras, J. Functional Analysis 9 (1972), 306–321. MR 0303307, DOI 10.1016/0022-1236(72)90004-3
- Makoto Tsukada, Strong convergence of martingales in von Neumann algebras, Proc. Amer. Math. Soc. 88 (1983), no. 3, 537–540. MR 699429, DOI 10.1090/S0002-9939-1983-0699429-6
- Hisaharu Umegaki, Conditional expectation in an operator algebra, Tohoku Math. J. (2) 6 (1954), 177–181. MR 68751, DOI 10.2748/tmj/1178245177
- Hisaharu Umegaki, Conditional expectation in an operator algebra. II, Tohoku Math. J. (2) 8 (1956), 86–100. MR 90789, DOI 10.2748/tmj/1178245011
- Alfons van Daele, A Radon Nikodým theorem for weights on von Neumann algebras, Pacific J. Math. 61 (1975), no. 2, 527–542. MR 410408
Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 282 (1984), 791-798
- MSC: Primary 46L50
- DOI: https://doi.org/10.1090/S0002-9947-1984-0732120-1
- MathSciNet review: 732120