A metric on the space of projections admitting nice isometries

• Autorzy: Lajos Molnár , Werner Timmermann
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B49: Transformers, preservers (operators on spaces of operators)
• 54E40: Special maps on metric spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 191
• Numer: 3
• Strony: 271-281

Daty

wydano

2009

Twórcy

autor

Lajos Molnár

• Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary

autor

Werner Timmermann

• Institut für Analysis, Technische Universität Dresden, D-01062 Dresden, Germany

Identyfikatory

DOI

10.4064/sm191-3-8