On the algebraic structure of the unitary group

Autores: Eric Ricard, Christian Rosendal
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 58, Fasc. 2, 2007, págs. 181-192
Idioma: inglés
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Resumen
- We consider the unitary group U of complex, separable, infinitedimensional Hilbert space as a discrete group. It is proved that, wheneverUacts 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.