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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 $\dim\cal H \geqslant 3$.

47B49Transformers, preservers (operators on spaces of operators)
81Q10Selfadjoint operator theory in quantum theory, including spectral analysis
Full Text: DOI
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