On order automorphisms of the effect algebra
Tóm tắt
We give short proofs of two descriptions given by Šemrl of order automorphisms of the effect algebra. This sheds new light on both formulas that look quite complicated. Our proofs rely on Molnár’s characterization of order automorphisms of the cone of all positive operators.
Tài liệu tham khảo
L. Molnár, Order-automorphisms of the set of bounded observables, J. Math. Phys., 42 (2001), 5904–5909.
L. Molnár, Selected Preserver Problems on Algebraic Structures of Linear Operators and on Function Spaces, Lect. Notes Math. 1895, Springer-Verlag, 2007.
P. Šemrl, Comparability preserving maps on Hilbert space effect algebras, Comm. Math. Phys., 313 (2012), 375–384.
P. Šemrl, Order isomorphisms of operator intervals, Integral Equations Operator Theory, 89 (2017), 1–42.
P. Šemrl, Groups of order automorphisms of operator intervals, Acta Sci. Math. (Szeged), 84 (2018), 125–136.