Duke Mathematical Journal

The Gelfand-Naimark theorem for JB-triples

Yaakov Friedman and Bernard Russo

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J., Volume 53, Number 1 (1986), 139-148.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46H70: Nonassociative topological algebras [See also 46K70, 46L70]
Secondary: 17C65: Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 32M10: Homogeneous complex manifolds [See also 14M17, 57T15] 46G20: Infinite-dimensional holomorphy [See also 32-XX, 46E50, 46T25, 58B12, 58C10] 46K99: None of the above, but in this section 46L70: Nonassociative selfadjoint operator algebras [See also 46H70, 46K70]


Friedman, Yaakov; Russo, Bernard. The Gelfand-Naimark theorem for $JB^\ast$ -triples. Duke Math. J. 53 (1986), no. 1, 139--148. doi:10.1215/S0012-7094-86-05308-1. https://projecteuclid.org/euclid.dmj/1077304884

Export citation


  • [1] E. Alfsen and F. Shultz, Non-commutative spectral theory for affine function spaces on convex sets, Mem. Amer. Math. Soc. 6 (1976), no. 172, xii+120.
  • [2] E. Alfsen and F. Shultz, State spaces of Jordan algebras, Acta Math. 140 (1978), no. 3-4, 155–190.
  • [3] E. Alfsen, F. Shultz, and E. Størmer, A Gelfand-Neumark theorem for Jordan algebras, Advances in Math. 28 (1978), no. 1, 11–56.
  • [4] H. Araki and G. Elliott, On the definition of $C\sp\ast$-algebras, Publ. Res. Inst. Math. Sci. 9 (1973/74), 93–112.
  • [5] T. Barton and R. Timoney, Weak $^\ast$-continuity of Jordan triple products and applications, Math. Scand., to appear.
  • [6] R. Braun, W. Kaup, and H. Upmeier, A holomorphic characterization of Jordan $C\sp\ast$-algebras, Math. Z. 161 (1978), no. 3, 277–290.
  • [7] E. Cartan, Sur les domaines bornés homogenes de l'esplace de $n$ variables complexes, Abh. Math. Sem. Univ. Hamburg 11 (1935), 116–162.
  • [8] S. Dineen, The second dual of a $JB^\ast$-triple system, Math. Scand., to appear.
  • [9] Y. Friedman and B. Russo, Contractive projections on operator triple systems, Math. Scand. 52 (1983), no. 2, 279–311.
  • [10] Y. Friedman and B. Russo, Solution of the contractive projection problem, J. Funct. Anal. 60 (1985), no. 1, 56–79.
  • [11] Y. Friedman and B. Russo, Algèbres d'opérateurs sans ordre: solution du problème du projecteur contractif, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 9, 393–396.
  • [12] Y. Friedman and B. Russo, Structure of the predual of a $JBW\sp \ast$-triple, J. Reine Angew. Math. 356 (1985), 67–89.
  • [13] I. M. Gelfand and M. A. Neumark, On the imbedding of normed rings into the ring of operators in Hilbert space, Rec. Math. [Mat. Sbornik] N.S. 12(54) (1943), 197–213.
  • [14] H. Hanche-Olsen and E. Størmer, Jordan operator algebras, Monographs and Studies in Mathematics, vol. 21, Pitman (Advanced Publishing Program), Boston, MA, 1984.
  • [15] L. Harris, Bounded symmetric homogeneous domains in infinite dimensional spaces, Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973), Springer, Berlin, 1974, 13–40. Lecture Notes in Math., Vol. 364.
  • [16] L. Harris, A generalization of $C\sp\ast$-algebras, Proc. London Math. Soc. (3) 42 (1981), no. 2, 331–361.
  • [17] S. Heinrich, Ultraproducts in Banach space theory, J. Reine Angew. Math. 313 (1980), 72–104.
  • [18] G. Horn, Klassifikation der $JBW^\ast$-Tripel vom Typ I, PhD dissertation, Tübingen, December 1984.
  • [19] P. Jordan, J. von Neumann, and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. 35 (1934), 29–64.
  • [20] W. Kaup, Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), no. 1, 39–64.
  • [21] W. Kaup, A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983), no. 4, 503–529.
  • [22] W. Kaup, Contractive projections on Jordan $C\sp\ast$-algebras and generalizations, Math. Scand. 54 (1984), no. 1, 95–100.
  • [23] W. Kaup and H. Upmeier, An infinitesimal version of Cartan's uniqueness theorem, Manuscripta Math. 22 (1977), no. 4, 381–401.
  • [24] Max Koecher, An elementary approach to bounded symmetric domains, Rice University, Houston, Tex., 1969.
  • [25] O. Loos, Bounded symmetric domains and Jordan pairs, Lecture Notes, University of California, Irvine, 1977.
  • [26] O. Loos and K. McCrimmon, Speciality of Jordan triple systems, Comm. Algebra 5 (1977), no. 10, 1057–1082.
  • [27] F. Shultz, On normed Jordan algebras which are Banach dual spaces, J. Funct. Anal. 31 (1979), no. 3, 360–376.
  • [28] L. L. Stachó, A projection principle concerning biholomorphic automorphisms, Acta Sci. Math. (Szeged) 44 (1982), no. 1-2, 99–124.
  • [29] E. Størmer, Jordan algebras of type $\rm I$, Acta Math. 115 (1966), 165–184.
  • [30] H. Upmeier, Symmetric Banach manifolds and Jordan $C\sp\ast$-algebras, North-Holland Mathematics Studies, vol. 104, North-Holland Publishing Co., Amsterdam, 1985.
  • [31] S. Vagi, Harmonic analysis on Cartan and Siegel domains, Studies in harmonic analysis (Proc. Conf., DePaul Univ., Chicago, Ill., 1974) ed. J. M. Ash, Math. Assoc. Amer., Washington, D.C., 1976, 257–309. MAA Stud. Math., Vol. 13.
  • [32] J. P. Vigué, Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Application aux domaines bornés symétriques, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 2, 203–281.
  • [33] W. Kaup, Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension. I, Math. Ann. 257 (1981), no. 4, 463–486.