Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Hilbertian interpretations of manuals


Author: Stanley P. Gudder
Journal: Proc. Amer. Math. Soc. 85 (1982), 251-255
MSC: Primary 81B10; Secondary 03G12, 06C99
DOI: https://doi.org/10.1090/S0002-9939-1982-0652452-9
MathSciNet review: 652452
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We characterize manuals which admit an interpretation in a manual on a Hilbert space. This characterization is given in terms of a certain set of states that the manual supports.


References [Enhancements On Off] (What's this?)

  • [1] D. J. Foulis and C. H. Randall, Operational statistics. I. Basic concepts, J. Math. Phys. 13 (1972), 1667-1675. MR 0416417 (54:4491)
  • [2] -, Empirical logic and quantum mechanics, Synthese 29 (1974), 81-111.
  • [3] -, The empirical logic approach to the physical sciences, in Foundations of Quantum Mechanics and Ordered Linear Spaces (A. Hartkämper and H. Neumann, Eds.), Springer-Verlag, New York, 1974. MR 0479146 (57:18594)
  • [4] -, Manuals, morphisms, and quantum mechanics, in Mathematical Foundations of Quantum Theory (A. R. Marlow, Ed.), Academic Press, New York, 1978. MR 0495822 (58:14470)
  • [5] S. Gudder, Stochastic methods in quantum mechanics, North-Holland, New York, 1979. MR 543489 (84j:81003)
  • [6] J. M. Jauch, Foundations of quantum mechanics, Addison-Wesley, Reading, Mass., 1968. MR 0218062 (36:1151)
  • [7] G. Mackey, The mathematical foundations of quantum mechanics, Benjamin, New York, 1963.
  • [8] C. H. Randall and D. J. Foulis, Operational statistics. II. Manuals of operations and their logics, J. Math. Phys. 14 (1973), 1472-1480. MR 0416418 (54:4492)
  • [9] -, A mathematical setting for inductive reasoning, in Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science (C. A. Hooker, Ed.), Reidel, Dordrecht, 1976.
  • [10] -, The operational approach to quantum mechanics, in The Logico-Algebraic Approach to Quantum Mechanics (C. A. Hooker, Ed.), Reidel, Dordrecht, 1977.
  • [11] V. Varadarajan, Geometry of quantum theory, Vol. I, Van Nostrand-Reinhold, Princeton, N.J., 1968. MR 0471674 (57:11399)
  • [12] R. Wright, Spin manuals, empirical logic talks quantum mechanics, in Mathematical Foundations of Quantum Theory (A. R. Marlow, Ed.), Academic Press, New York, 1978. MR 0503049 (58:19905)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 81B10, 03G12, 06C99

Retrieve articles in all journals with MSC: 81B10, 03G12, 06C99


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0652452-9
Keywords: Manuals, interpretations, Hilbert space, quantum logic
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society