References
O. Brateli and D. W. Robinson, Operator Algebras and Quantum StatisticalMechanics (Springer, Berlin, 1997), Vol.1.
K. Davidson and M. Kennedy, “Choquet order and hyperrigidity for function systems,” arXiv:1608.02334v1, 8 August 2016.
H. Halvorson, Deep Beauty: Understanding the Quantum World through Mathematical Innovation (Cambridge Univ. Press, Cambridge, 2011).
J. Hamhalter, “Isomorphisms of ordered structures of abelian C*-subalgebras of C*-subalgebras,” J.Math. Anal. Appl. 383, 391–399 (2011).
J. Hamhalter and E. Turilova, “Structure of associative subalgebras of Jordan operator algebras,” Quart. J. Math. 64, 397–408 (2013).
J. Hamhalter and E. Turilova, “Automorphisms of ordered structures of abelian parts of operator algebras and their role in quantum theory,” Int. J. Theor. Phys. 53, 3333–3345 (2014).
J. Hamhalter and E. Turilova, “Orthogonal measures on state spaces and context structures of quantum theory,” Int. J. Theor. Phys. 55, 3353–3365 (2016).
J. Hamhalter and E. Turilova, “Choquet order and Jordan morphisms of operator algebras,” Itogi Nauki Tekh., Ser.: Sovrem. Mat. Prilozh. 140, 119–124 (2017).
C. Heunen, N. P. Landsman, and B. Spitters, “Bohrification of operator algebras and quantum logic,” Synthese 186, 719–752 (2012).
R. V. Kadison and J. R. Ringrose, Theory of Operator Alegebras I, II (Academic, New York, 1986).
K. Landsman, Foundations of Quantum Theory, From Classical Concepts to Operator Algebras, Vol. 188 of Fundamental Theories of Physics (Springer Int., Switzerland, 2017).
B. Lindenhovius, PhD Thesis (Radbound Univ., Nijmegen, 2016).
J. Lukeš, J. Malý, I. Netuka, and J. Spurný, Integral Representation Theory, Applications to Convexity, Banach Spaces, and Potential Theory (de Gruyter, Berlin, New York, 2010).
R. Phelps, Lectures on Choquet’s Theorem (van Nostrand, Princeton, New Jersey, 1966).
M. Takesaki, Theory of Operator Algebras I, II, III (Springer, Berlin Heidelberg, 2001).
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Hamhalter, J., Turilova, E. Choquet Order and Jordan Maps. Lobachevskii J Math 39, 340–347 (2018). https://doi.org/10.1134/S1995080218030149
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DOI: https://doi.org/10.1134/S1995080218030149