Advances in Pure Mathematics

Volume 8, Issue 5 (May 2018)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

Google-based Impact Factor: 0.50  Citations  h5-index & Ranking

The Unitary Group in Its Strong Topology

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DOI: 10.4236/apm.2018.85029    940 Downloads   1,895 Views  Citations

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.

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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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