Uniqueness Results for the Infinite Unitary, Orthogonal and Associated Groups

Description:

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.

Creator(s): Atim, Alexandru Gabriel
Creation Date: May 2008
Partner(s):
UNT Libraries
Collection(s):
UNT Theses and Dissertations
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Publisher Info:
Publisher Name: University of North Texas
Place of Publication: Denton, Texas
Date(s):
  • Creation: May 2008
  • Digitized: July 18, 2008
Description:

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.

Degree:
Level: Doctoral
Discipline: Mathematics
Language(s):
Subject(s):
Keyword(s): Polish topological group | unitary operator | star-automorphism
Contributor(s):
Partner:
UNT Libraries
Collection:
UNT Theses and Dissertations
Identifier:
  • OCLC: 263684597 |
  • ARK: ark:/67531/metadc6136
Resource Type: Thesis or Dissertation
Format: Text
Rights:
Access: Public
License: Copyright
Holder: Atim, Alexandru Gabriel
Statement: Copyright is held by the author, unless otherwise noted. All rights reserved.