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The Universal Enveloping Ternary Ring of Operators of a JB*-Triple System

Published online by Cambridge University Press:  22 November 2013

Dennis Bohle  and
Wend Werner
Dennis Bohle
Affiliation:
Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität, Einsteinstraße 62, 48149 Münster, Germany, ([email protected]; [email protected])
Wend Werner
Affiliation:
Fachbereich Mathematik und Informatik, Westfälische Wilhelms-Universität, Einsteinstraße 62, 48149 Münster, Germany, ([email protected]; [email protected])
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Abstract

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We associate to every JB*-triple system a so-called universal enveloping ternary ring of operators (TRO). We compute the universal enveloping TROs of the finite dimensional Cartan factors.

Keywords

JC*-triple systemJ*-algebraCartan factorternary ring of operatorsternary algebrauniversal enveloping TROPrimary 17C6546L70
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 57 , Issue 2 , June 2014 , pp. 347 - 366
Copyright
Copyright © Edinburgh Mathematical Society 2014 

References

1.Alfsen, E. M. and Shultz, F. W., Geometry of state spaces of operator algebras, Mathematics: Theory and Applications (Birkhäuser, 2003).Google Scholar
2.Bohle, D., K-theory for ternary structures, PhD Thesis, Westfälische Wilhelms-Universität (2011).Google Scholar
3.Bohle, D. and Werner, W., A K-theoretic approach to the classification of symmetric spaces, preprint (2011).Google Scholar
4.Bunce, L. J. and Chu, C.-H., Compact operations, multipliers and Radon-Nikodým property in JB*-triples, Pac. J. Math. 153(2) (1992), 249–265.Google Scholar
5.Bunce, L. J., Feely, B. and Timoney, R., Operator space structure of JC*-triples and TROs, I, Math. Z. 270 (2012), 961–982.Google Scholar
6.Dang, T. and Friedman, Y., Classification of JBW*-triple factors and applications, Math. Scand. 61 (1987), 292–330.Google Scholar
7.Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space, Math. Scand. 59 (1986), 131–142.Google Scholar
8.Friedman, Y. and Russo, B., The Gelfand-Naĭmark theorem for JB*-triples, Duke Math. J. 53 (1986), 139–148.Google Scholar
9.Hanche-Olsen, H. and Stłrmer, E., Jordan operator algebras, Monographs and Studies in Mathematics, Volume 21 (Pitman, Boston, MA, 1984).Google Scholar
10.Horn, G., Characterization of the predual and ideal structure of a JBW*-triple, Math. Scand. 61 (1987), 117–133.Google Scholar
11.Isidro, J.-M., A glimpse at the theory of Jordan-Banach triple systems, Rev. Mat. Complut. 2 (1989), 145–156.Google Scholar
12.Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), 503–529.CrossRefGoogle Scholar
13.Kaup, W., On JB**-triples defined by fibre bundles, Manuscr. Math. 87 (1995), 379–403.CrossRefGoogle Scholar
14.Loos, O., Representations of Jordan triples, Trans. Am. Math. Soc. 185 (1973), 199–211.Google Scholar
15.Meyberg, K., Lectures on algebras and triple systems (The University of Virginia, Charlottesville, VA, 1972).Google Scholar
16.Neal, M. and Russo, B., Contractive projections and operator spaces, Trans. Am. Math. Soc. 355(6) (2003), 2223–2262.Google Scholar
17.Neal, M. and Russo, B., Representation of contractively complemented Hilbertian operator spaces on the Fock space, Proc. Am. Math. Soc. 134(2) (2006), 475–485.CrossRefGoogle Scholar
18.Neher, E., On the radical of J*-triples, Math. Z. 211(2) (1992), 323–332.Google Scholar
19.Upmeier, H., Symmetric Banach manifolds and Jordan C*-algebras, North-Holland Mathematics Studies, Volume 104 (North-Holland, Amsterdam, 1985).Google Scholar