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

Hiroshi Ando, and Yasumichi Matsuzawa. "Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects." Banach Center Publications 96.1 (2011): 35-50. <http://eudml.org/doc/286460>.

@article{HiroshiAndo2011,
abstract = {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.},
author = {Hiroshi Ando, Yasumichi Matsuzawa},
journal = {Banach Center Publications},
keywords = {finite von Neumann algebra; unitary group; affiliated operator; measurable operator; strong resolvent topology; tensor category; Lie group; Lie algebra},
language = {eng},
number = {1},
pages = {35-50},
title = {Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects},
url = {http://eudml.org/doc/286460},
volume = {96},
year = {2011},
}

TY - JOUR
AU - Hiroshi Ando
AU - Yasumichi Matsuzawa
TI - Existence of infinite-dimensional Lie algebra for a unitary group on a Hilbert space and related aspects
JO - Banach Center Publications
PY - 2011
VL - 96
IS - 1
SP - 35
EP - 50
AB - 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.
LA - eng
KW - finite von Neumann algebra; unitary group; affiliated operator; measurable operator; strong resolvent topology; tensor category; Lie group; Lie algebra
UR - http://eudml.org/doc/286460
ER -