# 效应代数的局部E-自同构Local E-Automorphisms on Effect Algebras

Abstract: In this paper, it is proved that each surjective two local E-automorphism on effect algebras  E(H) of Hilbert space H which dimension is equal to or more than three is E-automorphism and each surjective and linear two local E-automorphism on real space Bs(H)  is not only a Jordan automorphism but also has the form  , where U is unitary or anti-unitary operator.

[1] P. Busch, M. Grabowski and P. J. Lahti. Operational quantum physics. Berlin-Heidelberg-New York: Springer-Verlag, 1995.

[2] K. Kraus. State, effects and operations. Lecture Notes in Physics, Vol. 190. Berlin-Heidelberg-New York: Springer-Verlag, 1983.

[3] L. Molnár. Local automorphisms of some quantum mechanical structures. Journal of Mathematical Physics, 2001, 58(2): 91-100.

[4] R. V. Kadison. Local derivations. Journal of Algebra, 1990, 130(2): 494-509.

[5] P. Semrl. Local automorphisms and derivations on B(H). Proceedings of the American Mathematical Society, 1997, 125(9): 183-193.

[6] L. Molnár. Sequential isomorphismsbetween the sets of Von Neumann algebra effects. Acta Mathematica Scientia, 2003, 69(2-3): 755-772.

[7] G. Ludwig. Fundation of quantum mechanics. Berlin: Springer Verlag, 1983.

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