Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects

Tom 96 / 2011

Hiroshi Ando, Yasumichi Matsuzawa Banach Center Publications 96 (2011), 35-50 MSC: 22E65, 46L51. DOI: 10.4064/bc96-0-2


We show that for any strongly closed subgroup of a unitary group of a finite von Neumann algebra, there exists a canonical Lie algebra which is complete with respect to the strong resolvent topology. Our analysis is based on the comparison between measure topology induced by the tracial state and the strong resolvent topology we define on the particular space of closed operators on the Hilbert space. This is an expository article of the paper by both authors in Hokkaido Math. J. 41 (2012), 31–99, with some open problems.


  • Hiroshi AndoUniversity of Copenhagen, Denmark
    Research Institute for Mathematical Sciences, Kyoto University
    Kyoto, 606-8502, Japan
  • Yasumichi MatsuzawaMathematisches Institut, Universität Leipzig
    Johannisgasse 26, 04103 Leipzig, Germany
    Department of Mathematics, Hokkaido University
    Kita 10, Nishi 8, Kita-ku, Sapporo, 060-0810, Japan

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