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February 2012 Lie group-Lie algebra correspondences of unitary groups in finite von Neumann algebras
Hiroshi ANDO, Yasumichi MATSUZAWA
Hokkaido Math. J. 41(1): 31-99 (February 2012). DOI: 10.14492/hokmj/1330351338

Abstract

We give an affirmative answer to the question whether there exist Lie algebras for suitable closed subgroups of the unitary group U($¥mathcal{H}$) in a Hilbert space $¥mathcal{H}$ with U($¥mathcal{H}$) equipped with the strong operator topology. More precisely, for any strongly closed subgroup G of the unitary group U($¥mathfrak{M}$) in a finite von Neumann algebra $¥mathfrak{M}$, we show that the set of all generators of strongly continuous one-parameter subgroups of G forms a complete topological Lie algebra with respect to the strong resolvent topology. We also characterize the algebra $¥overline{¥mathfrak{M}}$ of all densely defined closed operators affiliated with $¥mathfrak{M}$ from the viewpoint of a tensor category.

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Hiroshi ANDO. Yasumichi MATSUZAWA. "Lie group-Lie algebra correspondences of unitary groups in finite von Neumann algebras." Hokkaido Math. J. 41 (1) 31 - 99, February 2012. https://doi.org/10.14492/hokmj/1330351338

Information

Published: February 2012
First available in Project Euclid: 27 February 2012

zbMATH: 1246.22024
MathSciNet: MR2920098
Digital Object Identifier: 10.14492/hokmj/1330351338

Subjects:
Primary: 22E65
Secondary: 46L51

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics

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Vol.41 • No. 1 • February 2012
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