Conditional expectations in von Neumann algebras and a theorem of Takesaki

Journal of Functional Analysis - Tập 45 - Trang 245-273 - 1982
Luigi Accardi1,2
1Istituto di Cibernetica del CNR, Arco Felice, Napoli, Italy
2Dipartimento di Matematica, Università di Roma II, Italy

Tài liệu tham khảo

Accardi, 1974, Non commutative Markov chains Accardi, 1981, Topics on quantum probability, Phys. Rep., 10.1016/0370-1573(81)90070-3 L. Accardi, and A. Frigerio, Markovian cocycles, Proc. Roy. Irish Acad., to appear. Albeverio, 1978, Frobenius theory for positive maps of von Neumann algebras, Comm. Math. Phys., 64, 83, 10.1007/BF01940763 Araki, 1973, Positive cone, Radon-Nikodym theorems, relative Hamiltonian and the Gibbs condition in statistical mechanics. An application of the Tomita-Tokesaki theory Araki, 1975, Introduction to relative Hamiltonian and relative entropy Bratteli, 1976, Unbounded derivations of von Neumann algebras, Ann. Inst. H. Poincaré Sect. A (N. S.), 25, 139 C. Cecchini, The ϑ-conditional expectation for weights, to appear. Combes, 1971, Poids Associé à une algèbre Hilbertienne à Gauche, Compositio Math., 23, 49 Connes, 1973, Sur le théorème de Radon-Nikodym pour le poids normaux fidèles semifinies, Bull. Soc. Math. France 2-ème Sér., 97, 253 Connes, 1973, Une classification des facteurs de type III, Ann. Sci. École Norm. Sup. 4-ème Série, 10.24033/asens.1247 Connes, 1976, Classification of injective factors. Cases II1, II∞, IIIλ, λ ≠ 1, Ann. of Math. III Sér., 104, 73, 10.2307/1971057 Davies, 1970, On the repeated measurement of continuous observables in Quantum Mechanics, J. Funct. Anal., 6, 318, 10.1016/0022-1236(70)90064-9 Demoen, 1980, Implementable positive maps on standard forms, J. Funt. Anal., 38, 354, 10.1016/0022-1236(80)90070-1 Dixmier, 1969 Dixmier, 1953, Formes linéaires sur un Anneau d'Opérateurs, Bull. Soc. Math. France, 81, 9, 10.24033/bsmf.1436 Dunford, 1963 Evans, 1977, Irreducible quantum dynamical semigroups, Comm. Math. Phys., 54, 293, 10.1007/BF01614091 Evans, 1979, Completely positive quasi free maps on the C.A.R. algebra, Comm. Math. Phys., 70, 53, 10.1007/BF01220502 Frigerio, 1977, Quantum dynamical semigroups and approach to equilibrium, Lett. Math. Phys., 2, 79, 10.1007/BF00398571 Golodez, 1972, Conditional expectations and modular automorphisms of von Neumann algebras, Funct. Anal. Appl., 6, 68 Gudder, 1977, Conditional expectations on von Neumann algebras: A new approach, Rep. Math. Phys., 12, 317, 10.1016/0034-4877(77)90030-1 Haag, 1976, On the equilibrium states in quantum statistical mechanics, Comm. Math. Phys., 5, 215, 10.1007/BF01646342 Hakeda, 1967, On some extension properties of von Neumann algebras, Tohoku Math., 19, 315, 10.2748/tmj/1178243281 Kadison, 1952, A generalized Schwarz inequality and algebraic invariants for operator algebra, Ann. of Math., 56, 494, 10.2307/1969657 Kossakowski, 1977, Quantim detailed balance and KMS condition, Comm. Math. Phys., 57, 97, 10.1007/BF01625769 Moy, 1954, Characterizations of conditional expectation as a transformation of function spaces, Pacific J. Mqath., 4, 47, 10.2140/pjm.1954.4.47 Nakamura, 1954, Expectations in an operator algebra, Tokohu Math. J., 6, 174, 10.2748/tmj/1178245176 Reed, 1972, Vol. I Sirugue, 1970, Constraints imposed upon a state of a system that satisfies the K.M.S boundary condition, Comm. math. Phys., 19, 161, 10.1007/BF01646632 Takesaki, 1970, Tomita's Theory of Modular Hilbert Algebras and its Applications, 10.1007/BFb0065832 Takesaki, 1972, Conditional Expectations in von Neumann Algebras, J. Funct. Anal., 9, 306, 10.1016/0022-1236(72)90004-3 Takesaki, 1971, States and Automorphism of Operator algebras, standard representations and the Kubo-Martin-Schwinger Boundary Condition, Springer Lecture Notes in Physics 20 Tomiyama, 1957, On the projection of norm, one in W∗-algebras, 33, 608 Tomiyama, 1958, On the projection of norm one in W∗-algebras, II, Tokohu Math. J., 10, 204, 10.2748/tmj/1178244714 Tomijama, 1959, On the projection of norm one in W∗-algebras, III, Tokohu Math. J., 11, 125, 10.2748/tmj/1178244633 Umegaki, 1954, Conditional expectation in an operator algebra, Tokohu Math. J., 6, 177, 10.2748/tmj/1178245177 Umegaki, 1956, Conditional expectation in an operator algebra, II, Tokohu Math. J., 8, 86, 10.2748/tmj/1178245011 Umegaki, 1959, Conditional expectation in an operator algebra, III, 11, 51 Umegaki, 1962, Conditional expectation in an operator algebra, IV, 14, 59 Van Daele, 1974, A new approach to Tomita-Takesaki theory of generalized Hilbert Algebras, J. Funct. Anal., 15, 378, 10.1016/0022-1236(74)90029-9 Von Neumann, 1961, On rings of operator, III, Vol. III, 161