A metric on the space of projections admitting nice isometries

Lajos Molnár, and Werner Timmermann. "A metric on the space of projections admitting nice isometries." Studia Mathematica 191.3 (2009): 271-281. <http://eudml.org/doc/284888>.

@article{LajosMolnár2009,
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.},
author = {Lajos Molnár, Werner Timmermann},
journal = {Studia Mathematica},
keywords = {Hilbert space; projections; Santos metric; gap metric; surjective isometries},
language = {eng},
number = {3},
pages = {271-281},
title = {A metric on the space of projections admitting nice isometries},
url = {http://eudml.org/doc/284888},
volume = {191},
year = {2009},
}

TY - JOUR
AU - Lajos Molnár
AU - Werner Timmermann
TI - A metric on the space of projections admitting nice isometries
JO - Studia Mathematica
PY - 2009
VL - 191
IS - 3
SP - 271
EP - 281
AB - 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.
LA - eng
KW - Hilbert space; projections; Santos metric; gap metric; surjective isometries
UR - http://eudml.org/doc/284888
ER -