# On the algebraic structure of the unitary group.

Éric Ricard; Christian Rosendal

Collectanea Mathematica (2007)

- Volume: 58, Issue: 2, page 181-192
- ISSN: 0010-0757

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topRicard, 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 -

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