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

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Ando H., Matsuzawa Y.

Banach Center Publications

2011

tom 96

nr 1

35-50

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.

Ograniczanie wyników

1 Banach Center Publications

1 Ando H.

1 Matsuzawa Y.

1 2011

Wyniki wyszukiwania

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