### Abstract

In the earlier paper (Molnár and Šemrl in Lett Math Phys 80:239–255, 2007), we described the structure of all spectral order automorphisms of the sets of Hilbert space effects and bounded observables in the case where the dimension of the underlying Hilbert space is at least 3. The aim of this note is to present a complete description in the missing two-dimensional case. We will see that in that case there is a one-to-one correspondence between the set of all spectral order automorphisms and the set of all bijective maps of pure states together with the set of all strictly increasing bijections of the real unit interval or the real line.

Original language | English |
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Pages (from-to) | 1-10 |

Number of pages | 10 |

Journal | Letters in Mathematical Physics |

DOIs | |

Publication status | Accepted/In press - Feb 29 2016 |

### Fingerprint

### Keywords

- effects
- observables
- spectral order

### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics

### Cite this

*Letters in Mathematical Physics*, 1-10. https://doi.org/10.1007/s11005-016-0830-1

**Spectral Order Automorphisms on Hilbert Space Effects and Observables : The 2-Dimensional Case.** / Molnár, L.; Nagy, Gergő.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Spectral Order Automorphisms on Hilbert Space Effects and Observables

T2 - The 2-Dimensional Case

AU - Molnár, L.

AU - Nagy, Gergő

PY - 2016/2/29

Y1 - 2016/2/29

N2 - In the earlier paper (Molnár and Šemrl in Lett Math Phys 80:239–255, 2007), we described the structure of all spectral order automorphisms of the sets of Hilbert space effects and bounded observables in the case where the dimension of the underlying Hilbert space is at least 3. The aim of this note is to present a complete description in the missing two-dimensional case. We will see that in that case there is a one-to-one correspondence between the set of all spectral order automorphisms and the set of all bijective maps of pure states together with the set of all strictly increasing bijections of the real unit interval or the real line.

AB - In the earlier paper (Molnár and Šemrl in Lett Math Phys 80:239–255, 2007), we described the structure of all spectral order automorphisms of the sets of Hilbert space effects and bounded observables in the case where the dimension of the underlying Hilbert space is at least 3. The aim of this note is to present a complete description in the missing two-dimensional case. We will see that in that case there is a one-to-one correspondence between the set of all spectral order automorphisms and the set of all bijective maps of pure states together with the set of all strictly increasing bijections of the real unit interval or the real line.

KW - effects

KW - observables

KW - spectral order

UR - http://www.scopus.com/inward/record.url?scp=84959362979&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959362979&partnerID=8YFLogxK

U2 - 10.1007/s11005-016-0830-1

DO - 10.1007/s11005-016-0830-1

M3 - Article

AN - SCOPUS:84959362979

SP - 1

EP - 10

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

SN - 0377-9017

ER -