The Unitary Group in Its Strong Topology  

作　　者：Martin Schottenloher 

机构地区：[1]Mathematisches Institut, LMU München, Theresienstr 39, München, Germany

出　　处：《Advances in Pure Mathematics》2018年第5期508-515,共8页理论数学进展（英文）

摘　　要：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.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.

关 键 词：UNITARY OPERATOR Strong OPERATOR Topology Topological GROUP Infinite Dimensional LIE GROUP CONTRACTIBILITY Hilbert BUNDLE Classifying Space 

分 类 号：O1[理学—数学]