Resumen de Short Geodesics of Unitaries in the L2 Metric

Esteban Andruchow

• Let M be a type II1 von Neumann algebra, t a trace in M, and l2 the GNS Hilbert space of t. We regard the unitary group UM as a subset of l2 and characterize the shortest smooth curves joining two fixed unitaries in the L2 metric. As a consequence of this we obtain that UM, though a complete (metric) topological group, is not an embedded riemannian submanifold of l2.