Spectral Order Automorphisms on Hilbert Space Effects and Observables: The 2-Dimensional Case

L. Molnár, Gergő Nagy

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-10
Number of pages10
JournalLetters in Mathematical Physics
DOIs
Publication statusAccepted/In press - Feb 29 2016

Fingerprint

automorphisms
Hilbert space
Automorphisms
intervals
Pure State
Bijective
One to one correspondence
Bijection
Real Line
Strictly
Interval
Unit

Keywords

  • effects
  • observables
  • spectral order

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

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

In: Letters in Mathematical Physics, 29.02.2016, p. 1-10.

Research output: Contribution to journalArticle

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