Resumen de On the algebraic structure of the unitary group

Eric Ricard, Christian Rosendal

• 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.