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Completely positive maps which are compact from L∞ to L1

Published online by Cambridge University Press:  28 June 2011

James A. Mingo
James A. Mingo
Affiliation:
Department of Mathematics and Statistics, Queen's University, Kingston, Ontario, K7L 3N6
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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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