On the algebraic structure of the unitary group

Details On the algebraic structure of the unitary group On the algebraic structure of the unitary group

2006-04-11

arxiv.org/abs/math/0604250v1

Mathematics

Functional Analysis

Scientific paper

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.

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