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Completely positive maps which are compact from L∞ to L1
Published online by Cambridge University Press: 28 June 2011
Abstract
We define a class of completely positive maps, closed under composition, on a von Neumann algebra. We show that when the algebra has no atomic part, the correspondences associated to this class of completely positive maps are disjoint from the identity correspondence. This enables one simultaneously to generalize the statement and simplify the proof of a theorem of A. Connes and V. F. R. Jones on factors of type II1 with property T.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 106 , Issue 2 , September 1989 , pp. 313 - 323
- Copyright
- Copyright © Cambridge Philosophical Society 1989
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