Geodesic
On the Structure and Tensor Products of JC-Algebras
Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1059-1074

Voir la notice de l'article provenant de la source Cambridge University Press

Norm closed (or weakly closed) Jordan algebras of self-adjoint operators on a Hilbert space were initially studied by Topping, Effros, and Stormer [15], [4], [12], [13]. These works are very “spatial”, in that the algebras are considered in one given representation. The introduction of their abstract counterparts, the JB- and JBW-algebras, has led to an increased interest in this subject. The author hopes this paper will support the view that a more “space-free” approach is fruitful, even if only the “concrete” algebras are under study. In accordance with this view, a “JC-algebra” in this paper will mean a normed Jordan algebra over the reals, which is isometrically isomorphic to a norm closed Jordan algebra of self-adjoint operators.Some of the results in this paper are closely related to, or rewordings of, results in the above-mentioned papers. However, I feel that the present approach is sufficiently different to be of interest in itself. In particular, many of the technical difficulties associated with earlier approaches are avoided. 
Hanche-Olsen, Harald. On the Structure and Tensor Products of JC-Algebras. Canadian journal of mathematics, Tome 35 (1983) no. 6, pp. 1059-1074. doi: 10.4153/CJM-1983-059-8
@article{10_4153_CJM_1983_059_8,
     author = {Hanche-Olsen, Harald},
     title = {On the {Structure} and {Tensor} {Products} of {JC-Algebras}},
     journal = {Canadian journal of mathematics},
     pages = {1059--1074},
     year = {1983},
     volume = {35},
     number = {6},
     doi = {10.4153/CJM-1983-059-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-059-8/}
}
TY  - JOUR
AU  - Hanche-Olsen, Harald
TI  - On the Structure and Tensor Products of JC-Algebras
JO  - Canadian journal of mathematics
PY  - 1983
SP  - 1059
EP  - 1074
VL  - 35
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-059-8/
DO  - 10.4153/CJM-1983-059-8
ID  - 10_4153_CJM_1983_059_8
ER  - 
%0 Journal Article
%A Hanche-Olsen, Harald
%T On the Structure and Tensor Products of JC-Algebras
%J Canadian journal of mathematics
%D 1983
%P 1059-1074
%V 35
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1983-059-8/
%R 10.4153/CJM-1983-059-8
%F 10_4153_CJM_1983_059_8

[1] 1. Alfsen, E. M., Shultz, F. W. and Stormer, E.. A Gelfand-Neumark theorem for Jordan algebras, Adv. Math. 28 (1978), 11–56. Google Scholar

[2] 2. Alfsen, E. M., Hanche-Olsen, H. and Shultz, F. W., State spaces of C*-algebras, Acta Math. 744 (1980), 267–305. Google Scholar

[3] 3. Edwards, C. M., Ideal theory in JB-algebras. J. London Math. Soc. (2) 16 (1977), 507–513. Google Scholar

[4] 4. Effros, E. and Stormer, E., Jordan algebras of self adjoint operators, Trans. Amer. Math. Soc. 727 (1967), 313–316. Google Scholar

[5] 5. Giordano, T., Antiautomorphisms involutifs des facteurs de von Neumann injectifs, thesis (1981). Google Scholar

[6] 6. Hanche-Olsen, H., A note on the bidual of a JB-algebra, Math. Zeit. 175 (1980), 29–31. Google Scholar

[7] 7. Hanche-Olsen, H., >Split faces and ideal structure of operator algebras, Math. Scand. 48 (1981), 137–144. Google Scholar

[8] 8. Kirillov, A. A., Elements of the theory of representations (Springer-Verlag, Berlin, Heidelberg, New York, 1976). Google Scholar | DOI

[9] 9. Robertson, A. G., Automorphisms of spin factors and decomposition of positive maps, Quart. J. Math. Oxford (2) 34 (1983), 87–96. Google Scholar

[10] 10. Shultz, F. W., On normed Jordan algebras which are Banach dual spaces, J. Funct. Anal. 31 (1979), 360–376. Google Scholar

[11] 11. Storrner, E., On the Jordan structure of C*-algebras, Trans. Amer. Math. Soc. 120 (1965), 438–447. Google Scholar

[12] 12. Storrner, E., Jordan algebras of type I, Acta Math. 115 (1966), 165–184. Google Scholar

[13] 13. Storrner, E., Irreducible Jordan algebras of self adjoint operators, Trans. Amer. Math. Soc. 130 (1968), 153–166. Google Scholar

[14] 14. Storrner, E., Real structure in the hyperfinite factor, Duke Math. J. 47 (1980), 145–154. Google Scholar

[15] 15. Topping, D., Jordan algebras of self adjoint operators, Mem. Amer. Math. Soc. 53 (1965). Google Scholar

[16] 16. Storrner, E., An isomorphism invariant for spin factors, J. Math. Mech. 75 (1966), 1055–1064. Google Scholar

Cité par Sources :