Kim, Sang Og Automorphisms of Hilbert space effect algebras. (English) Zbl 1072.47036 Linear Algebra Appl. 402, 193-198 (2005). 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 \(\phi:\mathcal E(\mathcal H)\to \mathcal E(\mathcal H)\) is conditionally multiplicative and conditionally additive, then \(\phi\) is implemented by a unitary or antiunitary operator on \(\mathcal H\). We also show that 2-local ortho-order automorphisms on \(\mathcal E(\mathcal H)\) are of the same form if \(\dim\mathcal H \geqslant 3\). Cited in 1 Document MSC: 47B49 Transformers, preservers (linear operators on spaces of linear operators) 81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis Keywords:Hilbert space effects; 2-local ortho-order automorphism PDFBibTeX XMLCite \textit{S. O. Kim}, Linear Algebra Appl. 402, 193--198 (2005; Zbl 1072.47036) Full Text: DOI 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), Springer: Springer Berlin · 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., \( \bot \)-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; 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.