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Positive extensions of automorphisms of spin factors

Published online by Cambridge University Press:  14 November 2011

A. Guyan Robertson
A. Guyan Robertson
Affiliation:
Department of Mathematics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ
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Synopsis

A spin factor is a JW-factor of type I2. It is shown that certain automorphisms of finite dimensional spin factors extend to extremal positive linear maps on complex matrix algebras which are not decomposable, and hence, do not preserve extreme rays of the positive cone.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 94 , Issue 1-2 , 1983 , pp. 71 - 77
Copyright
Copyright © Royal Society of Edinburgh 1983

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References

1Alfsen, E. M., Hanche-Olsen, H. and Shultz, F. W.. State spaces of C*-algebras. Acta Math. 144 (1980), 267–305.CrossRefGoogle Scholar
2Andersen, T. B.. On multipliers and order bounded operators in C*-algebras. Proc. Amer. Math. Soc. 25 (1970), 896–899.Google Scholar
3Arveson, W. B.. Subalgebras of C*-algebras. Acta Math. 123 (1969), 141–224.CrossRefGoogle Scholar
4Bratteli, O. and Robinson, D. W.. Operator Algebras and Quantum Statistical Mechanics II (New York: Springer, 1981).CrossRefGoogle Scholar
5Choi, M. D.. Some assorted inequalities for positive linear maps on C*-algebras. J. Operator Theory 4 (1980), 271–285.Google Scholar
6Effros, E. and StøSrmer, E.. Positive projections and Jordan structure in operator algebras. Math. Scand. 45 (1979), 127–138.CrossRefGoogle Scholar
7Hanche-Olsen, H.. On the structure and tensor products of JC-algebras, preprint (1981).Google Scholar
8Loewy, R. and Schneider, H.. Positive operators on the n-dimensional ice-cream cone. J. Math. Anal. Appl. 49 (1975), 375–392.CrossRefGoogle Scholar
9O'Brien, R. C.. On extreme matrices and extreme vectors of cones in Rn. Linear Algebra Appl. 12 (1975), 77–79.Google Scholar
10Robertson, A. G.. Automorphisms of spin factors and the decomposition of positive maps. Quart. J. Math. 34 (1983), 87–96.CrossRefGoogle Scholar
11Størmer, E.. Positive linear maps on operator algebras. Acta Math. 110 (1963), 233–278.CrossRefGoogle Scholar
12Størmer, E.. On the Jordan structure of C*-algebras. Trans. Amer. Math. Soc. 120 (1965), 438–447.Google Scholar
13Stølrmer, E.. Decomposition of positive projections on C*-algebras. Math. Ann. 247 (1980), 21–41.CrossRefGoogle Scholar
14Topping, D. M.. Jordan algebras of self-adjoint operators. Mem. Amer. Math. Soc. 53 (1965).Google Scholar
15Topping, D. M.. An isomorphism invariant for spin factors. J. Math. Mech. 15 (1966), 1055–1064.Google Scholar
16Upmeier, H.. Automorphism groups of Jordan C*-algebras. Math. Z. 176 (1981), 21–34.CrossRefGoogle Scholar
17Wright, J. D.M. and Youngson, M. A.. On isometries of Jordan algebras. J. London Math. Soc. 17 (1978), 339–344.Google Scholar
18Jacobson, N.. Basic Algebra II (San Francisco: Freeman, 1980).Google Scholar