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Extreme positive linear maps between Jordan Banach algebras

Published online by Cambridge University Press:  17 April 2009

Cho-Ho Chu  and
Nigel P. H. Jefferies
Cho-Ho Chu
Affiliation:
Department of Mathematical Sciences, University of London Goldsmiths' College, London SE14, United Kingdom.
Nigel P. H. Jefferies
Affiliation:
Department of Mathematical Sciences, University of London Goldsmiths' College, London SE14, United Kingdom.
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Abstract

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Let A and B be unital JB-algebras. We study the extremal structure of the convex set S (A,B) of all identity preserving positive linear maps from A to B. We show that every unital Jordan homomorphism from A to B is an extreme point of S (A,B). An extreme point of S (A,B) need not be a homomorphism and we show that, given A, every extreme point of S (A,B) is a homomorphism for any B if, and only if, dim A ≤ 2. We also determine when S (A,B) is a simplex.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 349 - 362
Copyright
Copyright © Australian Mathematical Society 1987

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