Appendix

Arveson, W.B.: Subalgebras of C*-Algebras. Acta Math. 123 (1969), 141–224.
Article MathSciNet MATH Google Scholar
Choi, M.-D.: Completely Positive Linear Maps on Complex Matrices. Lin. Alg. and Applic. 10 (1975), 285–290.
Article MathSciNet MATH Google Scholar
Evans, D.E.: Completely Positive Quasi-Free Maps on the CAR Algebra. Commun. Math. Phys. 70 (1979), 53–68.
Article MATH Google Scholar
Kern, M.; Nagel, R.; Palm, G.: Dilations of Positive Operators: Construction and Ergodic Theory. Math. Z. 156 (1977), 265–277.
Article MathSciNet MATH Google Scholar
Kümmerer, B.: Markov Dilations on W*-Algebras. Submitted to Journal of Functional Analysis. Some results of this paper are summarized in Kümmerer, B.: Markov Dilations of Completely Positive Operators on W*-Algebras. In Gr. Arsene (Ed.), "Dilation Theory, Toeplitz Operators, and Other Topics", Operator Theory: Advances and Applications, Vol 11 (Timisoara 1982), Birkhäuser Verlag, Basel, 251–259.
Google Scholar
Kümmerer, B.: Examples of Markov Dilations over the 2×2 Matrices. In L. Accardi, A. Frigerio, V. Gorini (Ed.), "Quantum Probability and Applications to the Quantum Theory of Irreversible Processes" (Frascati 1982), to appear in Lecture Notes in Mathematics, Springer Verlag, Berlin — Heidelberg — New York.
Google Scholar
Kümmerer, B. Representations of Completely Positive Operators. In preparation.
Google Scholar
Kümmerer, B.; Schröder, W.: A Markov Dilation of a Non — Quasifree Bloch Evolution. Commun. Math. Phys. 90 (1983), 251–262.
Article MATH Google Scholar
Kümmerer, B.; Schröder, W.: A Survey of Markov Dilations for the Spin — 1/2 — Relaxation and Physical Interpretation. Semesterbericht Funktionalanalysis. Wintersemester 1981/82, 187–213.
Google Scholar
Størmer, E.: Positive Linear Maps of Operator Algebras. Acta Math. 110 (1963), 233–278.
Article MathSciNet MATH Google Scholar
Sz.-Nagy, B.; Foias, C.: Harmonic Analysis of Operators on Hilbert Spaces. North Holland, Amsterdam 1970.
MATH Google Scholar
Takesaki, M.: Conditional Expectations in von Neumann Algebras. J. Functional Analysis 9 (1971), 306–321.
Article MathSciNet MATH Google Scholar
Takesaki, M.: The Structure of a von Neumann Algebra with a Homogeneous Periodic State. Acta Math. 131 (1973) 79–121.
Article MathSciNet MATH Google Scholar
Takesaki, M.: Theory of Operator Algebras I. Springer-Verlag, Berlin — Heidelberg — New York 1979.
Book MATH Google Scholar
Varilly, J.C.: Dilations of a Non-Quasifree Dissipative Evolution. Lett. Math. Phys. 5 (1981), 113–116.
Article MathSciNet MATH Google Scholar

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Department of Mathematics, Saitama University, Japan
Toshikazu Natsume

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Toshikazu Natsume
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Huzihiro Araki Calvin C. Moore Şerban-Valentin Stratila Dan-Virgil Voiculescu

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Natsume, T. (1985). Appendix. In: Araki, H., Moore, C.C., Stratila, ŞV., Voiculescu, DV. (eds) Operator Algebras and their Connections with Topology and Ergodic Theory. Lecture Notes in Mathematics, vol 1132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074891

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DOI: https://doi.org/10.1007/BFb0074891
Published: 16 September 2006
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15643-7
Online ISBN: 978-3-540-39514-0
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