Short geodesics of unitaries in the L2 metric
| Autor: | Esteban Andruchow |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2005 |
| Předmět: |
Trace (linear algebra)
Geodesic Matemáticas General Mathematics 010102 general mathematics Hilbert space 01 natural sciences Matemática Pura Combinatorics Algebra symbols.namesake Von Neumann algebra Unitary group INFINITE DIMENSIONAL RIEMANNIAN MANIFOLDS 0103 physical sciences Metric (mathematics) symbols 010307 mathematical physics Topological group 0101 mathematics SHORT GEODESICS Riemannian submanifold CIENCIAS NATURALES Y EXACTAS Mathematics UNITARY GROUP |
| Popis: | Let ℳ be a type II1 von Neumann algebra, τ a trace in ℳ, and L2 (ℳ, τ) the GNS Hilbert space of τ . We regard the unitary group Uℳ as a subset of L2(ℳ, τ) 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(ℳ, τ) |
| Databáze: | OpenAIRE |
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