Let H be a separable infinite dimensional complex Hilbert space, let U(H) be the Polish topological group of unitary operators on H, let G be a Polish topological group and φ:G→U(H) an algebraic isomorphism. Then φ is a topological isomorphism. The same theorem holds for the projective unitary group, for the group of *-automorphisms of L(H) and for the complex isometry group. If H is a separable real Hilbert space with dim(H)≥3, the theorem is also true for the orthogonal group O(H), for the projective orthogonal group and for the real isometry group. The theorem fails for U(H) if H is finite dimensional complex Hilbert space.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc6136 |
| Date | 05 1900 |
| Creators | Atim, Alexandru Gabriel |
| Contributors | Kallman, Robert, Bator, Elizabeth M., Lewis, Paul |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | Text |
| Rights | Public, Copyright, Atim, Alexandru Gabriel, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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