On the algebraic structure of the unitary group.

Ricard, Éric, and Rosendal, Christian. "On the algebraic structure of the unitary group.." Collectanea Mathematica 58.2 (2007): 181-192. <http://eudml.org/doc/41805>.

@article{Ricard2007,
abstract = {We consider the unitary group U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever U acts by isometries on a metric space, every orbit is bounded. Equivalently, U is not the union of a countable chain of proper subgroups, and whenever E ⊆ U generates U, it does so by words of a fixed finite length.},
author = {Ricard, Éric, Rosendal, Christian},
journal = {Collectanea Mathematica},
keywords = {Grupos de transformación; Grupo unitario; Espacios de Hilbert; Acotación; strong uncountable cofinality; Cayley boundedness; unitary group},
language = {eng},
number = {2},
pages = {181-192},
title = {On the algebraic structure of the unitary group.},
url = {http://eudml.org/doc/41805},
volume = {58},
year = {2007},
}

TY - JOUR
AU - Ricard, Éric
AU - Rosendal, Christian
TI - On the algebraic structure of the unitary group.
JO - Collectanea Mathematica
PY - 2007
VL - 58
IS - 2
SP - 181
EP - 192
AB - We consider the unitary group U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever U acts by isometries on a metric space, every orbit is bounded. Equivalently, U is not the union of a countable chain of proper subgroups, and whenever E ⊆ U generates U, it does so by words of a fixed finite length.
LA - eng
KW - Grupos de transformación; Grupo unitario; Espacios de Hilbert; Acotación; strong uncountable cofinality; Cayley boundedness; unitary group
UR - http://eudml.org/doc/41805
ER -