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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 \(\phi:\mathcal E(\mathcal H)\to \mathcal E(\mathcal H)\) 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 \(\dim\mathcal H \geqslant 3\).

MSC:

47B49 Transformers, preservers (linear operators on spaces of linear operators)
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
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