A metric on the space of projections admitting nice isometries

Lajos Molnar, Werner Timmermann

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Motivated by the concept of separation between propositions in quantum logic, we introduce the so-called separation metric or Santos metric on the space of all projections in a Hilbert space. We show that the resulting metric space has only "nice" surjective isometries. On the nontrivial projections they are all unitarily or antiunitarily equivalent to the identity or to taking the orthogonal complement. We relate this result to Wigner's classical theorem on the form of quantum mechanical symmetry transformations.

Original languageEnglish
Pages (from-to)271-281
Number of pages11
JournalStudia Mathematica
Volume191
Issue number3
DOIs
Publication statusPublished - Jul 13 2009

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Keywords

  • Gap metric
  • Hilbert space
  • Projections
  • Santos metric
  • Surjective isometries

ASJC Scopus subject areas

  • Mathematics(all)

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