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The tensor product of generalized sample spaces which admit a unital set of dispersion-free weights

  • Part I. Invited Papers Dedicated To The Memory Of Charles H. Randall (1928–1987)
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Abstract

Techniques for constructing the tensor product of two generalized sample spaces which admit unital sets of dispersion-free weights are discussed. A duality theory is developed, based on the 1-cuts of the dispersion-free weights, and used to produce a candidate for the tensor product. This construction is verified for Dacification manuals, a conjecture is given for other reflexive cases, and some adjustments for nonreflexive cases are considered. An alternate approach, using graphs of interpretation morphisms on the duals, is also presented.

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References

  1. D. J. Foulis and C. H. Randall, “Empirical logic and tensor products,” inProceedings of the Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universität, Marburg, West Germany (1979).

    Google Scholar 

  2. C. H. Randall and D. J. Foulis, “Operational statistics and tensor products,” inProceedings, Colloquium on the Interpretations and Foundations of Quantum Theories, Fachbereich Physik der Philipps Universität, Marburg, West Germany (1979).

    Google Scholar 

  3. P. F. Lock and R. H. Lock, “Tensor product of generalized sample spaces,”Int. J. Theor. Phys. 23, 629–641 (1984).

    Google Scholar 

  4. R. H. Lock, “Constructing the tensor product of generalized sample spaces,” Ph. D. dissertation, University of Massachusetts at Amherst, 1981.

  5. P. R. Halmos,Finite-Dimensional Vector Spaces, Van Nostrand, New York, 1981), Sec. 25.

    Google Scholar 

  6. D. J. Foulis and C. H. Randall, “Manuals, morphisms, and quantum mechanics,” inMathematical Foundations of Quantum Mechanics, A. R. Marlow, ed. (Academic Press, New York, 1978).

    Google Scholar 

  7. C. H. Randall and D. J. Foulis, “A mathematical setting for inductive reasoning,” inFoundations of Probability Theory, Statistical Inference, and Statistical Theories of Science III, C. A. Hooker and W. D. Harper, eds. (Reidel Dordrecht, Holland, 1976).

    Google Scholar 

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Lock, R.H. The tensor product of generalized sample spaces which admit a unital set of dispersion-free weights. Found Phys 20, 477–498 (1990). https://doi.org/10.1007/BF01883236

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  • DOI: https://doi.org/10.1007/BF01883236

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