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Automorphisms of Hilbert space effect algebras. (English) Zbl 1072.47036
Summary: We consider bijections of the Hilbert space effect algebra that preserve the algebraic structures in one direction and have some other properties. It is shown that if $\phi:\cal E(\cal H)\to \cal E(\cal H)$ is conditionally multiplicative and conditionally additive, then $\phi$ is implemented by a unitary or antiunitary operator on $\cal H$. We also show that 2-local ortho-order automorphisms on $\cal E(\cal H)$ are of the same form if $\dim\cal H \geqslant 3$.

MSC:
47B49Transformers, preservers (operators on spaces of operators)
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
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References:
[1] Barczy, M.; Tóth, M.: Local automorphisms of the sets of states and effects on a Hilbert space. Rep. math. Phys. 48, 289-298 (2001) · Zbl 1007.47014
[2] Bunce, L. J.; Wright, D. M.: The MacKey-Gleason problem. Bull. amer. Math. soc. 26, 288-293 (1992) · Zbl 0759.46054
[3] Cassinelli, G.; De Vito, E.; Lahti, P.; Levrero, A.: A theorem of ludwig revisited. Found. phys. 30, 1755-1761 (2000)
[4] Ludwig, G.: Foundations of quantum mechanics, vol I. (1983) · Zbl 0509.46057
[5] Molnár, L.: Local automorphisms of some quantum mechanical structures. Lett. math. Phys. 58, 91-100 (2001) · Zbl 1002.46044
[6] Molnár, L.: On some automorphisms of the set of effects on Hilbert space. Lett. math. Phys. 51, 37-45 (2000) · Zbl 1072.81535
[7] Molnár, L.: The set of automorphisms of $B(H)$ is topologically reflexive in $B(B(H))$. Studia math. 122, 183-193 (1997) · Zbl 0871.47030
[8] Molnár, L.: Preservers on Hilbert space effects. Linear algebra appl. 370, 287-300 (2003) · Zbl 1040.47028
[9] Molnár, L.; Páles, Z.: ⊥-order automorphisms of Hilbert space effect algebras: the two-dimensional case. J. math. Phys. 42, 1907-1912 (2001) · Zbl 1025.47045
[10] L. Molnár, P. Šemrl, Conditional affine and conditional sequential automorphisms of the set of Hilbert space effects, preprint
[11] Šemrl, P.: Local automorphisms and derivations on $B(H)$. Proc. amer. Math. soc. 125, 2677-2680 (1997) · Zbl 0887.47030