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

• Autorzy: Hiroshi Ando , Yasumichi Matsuzawa
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46L51: Noncommutative measure and integration
• 22E65: Infinite-dimensional Lie groups and their Lie algebras: general properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2011
• Tom: 96
• Numer: 1
• Strony: 35-50

Daty

wydano

2011

Twórcy

autor

Hiroshi Ando

• University of Copenhagen, Denmark, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

autor

Yasumichi Matsuzawa

• Mathematisches Institut, Universität Leipzig, Johannisgasse 26, 04103 Leipzig, Germany, Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-ku, Sapporo, 060-0810, Japan

Identyfikatory

DOI

10.4064/bc96-0-2