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Irreducible positive linear maps
on operator algebras


Author: Douglas R. Farenick
Journal: Proc. Amer. Math. Soc. 124 (1996), 3381-3390
MSC (1991): Primary 46L05
DOI: https://doi.org/10.1090/S0002-9939-96-03441-7
MathSciNet review: 1340385
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Abstract: Motivated by the classical results of G. Frobenius and O. Perron on the spectral theory of square matrices with nonnegative real entries, D. Evans and R. Høegh-Krohn have studied the spectra of positive linear maps on general (noncommutative) matrix algebras. The notion of irreducibility for positive maps is required for the Frobenius theory of positive maps. In the present article, irreducible positive linear maps on von Neumann algebras are explicitly constructed, and a criterion for the irreducibility of decomposable positive maps on full matrix algebras is given.


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Additional Information

Douglas R. Farenick
Affiliation: Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, Canada S4S 0A2
Email: farenick@abel.math.uregina.ca

DOI: https://doi.org/10.1090/S0002-9939-96-03441-7
Keywords: Positive linear maps, irreducibilty, completely positive maps
Received by editor(s): May 2, 1995
Additional Notes: This work is supported in part by a grant from The Natural Sciences and Engineering Research Council of Canada.
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society

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