Short Geodesics of Unitaries in the <i>L</i><sup>2</sup> Metric

Esteban Andruchow

Type: Article

Publication Date: 2005-09-01

Citations: 12

DOI: https://doi.org/10.4153/cmb-2005-032-0

Abstract

Abstract Let ℳ be a type II 1 von Neumann algebra, τ a trace in ℳ, and L 2 (ℳ, τ) the GNS Hilbert space of τ . We regard the unitary group U ℳ as a subset of L 2 (ℳ, τ) and characterize the shortest smooth curves joining two fixed unitaries in the L 2 metric. As a consequence of this we obtain that U ℳ , though a complete (metric) topological group, is not an embedded riemannian submanifold of L 2 (ℳ, τ)

Locations

Canadian Mathematical Bulletin - View - PDF
CONICET Digital (CONICET) - View - PDF

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