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Article Dans Une Revue Collectanea Mathematica Année : 2007

On the algebraic structure of the unitary group

Résumé

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 $\E\subseteq \U$ generates $\U$, it does so by words of a fixed finite length.

Dates et versions

hal-00475226 , version 1 (21-04-2010)

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Éric Ricard, Christian Rosendal. On the algebraic structure of the unitary group. Collectanea Mathematica, 2007, 58 (2), pp.181-192. ⟨hal-00475226⟩
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