Abstract
The set of all effects on a Hilbert space has an affine structure (it is a convex set) as well as a multiplicative structure (it can be equipped with the so-called Jordan triple product). In this paper we describe the corresponding automorphisms of that set.
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References
Bresšar, M. and SŠmrl, P.: Mappings which preserve idempotents, local automorphisms, and local derivations, Canad. J. Math. 45 (1993), 483–496.
Busch, P. and Gudder, S. P.: Effects as functions on projective Hilbert space, Lett. Math. Phys. 47 (1999), 329–337.
Cassinelli, G., De Vito, E., Lahti P. J. and Levrero, A.: Symmetry groups in quantum mechanics and the theorem of Wigner on the symmetry transformations, Rev. Math. Phys. 9 (1997), 921–941.
Cassinelli, G., De Vito, E., Lahti P. J. and Levrero, A.: A theorem of Ludwig revisited, Preprint.
Gudder, S. P.: Morphisms, tensor products and σ-effect algebras, Rep. Math. Phys. 42 (1998), 321–346.
Gudder, S. P. and Pulmannová, S.: Representation theorem for convex effect algebras, Comment. Math. Univ. Carolinae 39 (1998), 645–659.
Herstein, I. N.: Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331–341.
Ludwig, G.: Foundations of Quantum Mechanics, Vol. I, Springer, New York, 1983.
Martindale, W. S. III: When are multiplicative mappings additive?, Proc.Amer. Math. Soc. 21 (1969), 695–698.
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Molnár, L. On Some Automorphisms of the Set of Effects on Hilbert Space. Letters in Mathematical Physics 51, 37–45 (2000). https://doi.org/10.1023/A:1007631827940
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DOI: https://doi.org/10.1023/A:1007631827940