Short Geodesics of Unitaries in the L2 Metric

• Autores: Esteban Andruchow
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 3, 2005, págs. 340-355
• Idioma: inglés
• DOI: 10.4153/cmb-2005-032-0
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• Resumen

  • 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.