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An extreme positive operator on a polyhedral cone

Published online by Cambridge University Press:  18 May 2009

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, King's Buildings, Mayfield Road, Edinburgh EH9 3JZ
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In [2], R. Loewy and H. Schneider studied positive linear operators on circular cones. They characterised the extremal positive operators on these cones and noticed that such operators preserve the set of extreme rays of the cone in this case. They then conjectured that this property of extremal positive operators is true in general.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 30 , Issue 3 , September 1988 , pp. 347 - 348
Copyright
Copyright © Glasgow Mathematical Journal Trust 1988

References

1.Choi, M. D. and Lam, T. Y., Extremal positive semidefinite forms, Math. Ann. 231 (1977) 1–18.Google Scholar
2.Loewy, R. and Schneider, H., Positive operators on the n-dimensional ice-cream cone, J. Math. Anal. Appl. 49 (1975) 375–392.Google Scholar
3.O'Brien, R. C., On extreme matrices and extreme vectors of cones in ℝn, Linear Algebra Appl. 12 (1975) 77–79.Google Scholar
4.Robertson, A. G., Schwarz inequalities and the decomposition of positive maps on C*-algebras, Math. Proc. Camb. Phil. Soc. 94 (1983) 291–296.Google Scholar