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The Unitary Group in Its Strong Topology
Mathematisches Institut, LMU München, Theresienstr 39, München, Germany
- 1 Mathematisches Institut, LMU München, Theresienstr 39, München, Germany
Advances in Pure Mathematics·Volume 08 (2018)·Pages 508–515·Published 9 May 2018·DOI10.4236/apm.2018.85029
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Abstract
The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.
KeywordsUnitary OperatorStrong Operator TopologyTopological GroupInfinite Dimensional Lie GroupContractibilityHilbert BundleClassifying Space
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