作者
Stephen D Barreto, BV Rajarama Bhat, Volkmar Liebscher, Michael Skeide
发表日期
2004/7/1
期刊
Journal of Functional Analysis
卷号
212
期号
1
页码范围
121-181
出版商
Academic Press
简介
Christensen and Evans showed that, in the language of Hilbert modules, a bounded derivation on a von Neumann algebra with values in a two-sided von Neumann module (i.e. a sufficiently closed two-sided Hilbert module) are inner. Then they use this result to show that the generator of a normal uniformly continuous completely positive (CP-) semigroup on a von Neumann algebra decomposes into a (suitably normalized) CP-part and a derivation like part. The backwards implication is left open. In these notes we show that both statements are equivalent among themselves and equivalent to a third one, namely, that any type I tensor product system of von Neumann modules has a unital central unit. From existence of a central unit we deduce that each such product system is isomorphic to a product system of time ordered Fock modules. We, thus, find the analogue of Arveson's result that type I product systems of …
引用总数
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学术搜索中的文章
SD Barreto, BVR Bhat, V Liebscher, M Skeide - Journal of Functional Analysis, 2004