The Unitary Group in Its Strong Topology - Advances in Pure Mathematics

APM > Vol.8 No.5, May 2018

The Unitary Group in Its Strong Topology ()

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DOI: 10.4236/apm.2018.85029 950 Downloads 1,910 Views Citations

Author(s)

Martin Schottenloher

Affiliation(s)

Mathematisches Institut, LMU München, Theresienstr 39, München, Germany.

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.

KEYWORDS

Unitary Operator, Strong Operator Topology, Topological Group, Infinite Dimensional Lie Group, Contractibility, Hilbert Bundle, Classifying Space

Share and Cite:

Schottenloher, M. (2018) The Unitary Group in Its Strong Topology. Advances in Pure Mathematics, 8, 508-515. doi: 10.4236/apm.2018.85029.

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