A holomorphic characterization of Jordan \(C^*\)-algebras. (English) Zbl 0385.32002


32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
17C50 Jordan structures associated with other structures
46L05 General theory of \(C^*\)-algebras
46H20 Structure, classification of topological algebras
46H99 Topological algebras, normed rings and algebras, Banach algebras
Full Text: DOI EuDML


[1] Alfsen, E.M., Shultz, F.W.: State spaces of Jordan Algebras. Acta Math. (to appear) · Zbl 1257.81006
[2] Alfsen, E.M., Shultz, F.W., Størmer, E.: A Gelfand-Neumark theorem for Jordan algebras. Advances in Math.28, 11-56 (1978) · Zbl 0397.46065
[3] Bonsall, F.F., Duncan, J.: Complete Normed Algebras. Ergebnisse der Mathematik und ihrer Grenzgebiete, Bd. 80. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0271.46039
[4] Braun, H., Koecher, M.: Jordan-Algebren. Grundlehren der Mathematischen Wissenschaften, Bd. 128. Berlin-Heidelberg-New York: Springer 1965
[5] Harris, L.A.: Bounded symmetric homogeneous domains in infinite dimensional spaces. Proceedings on Infinite Dimensional Holomorphy. Lexington 1973), pp. 13-40. Lecture Notes in Mathematics364. Berlin-Heidelberg-New York: Springer 1974
[6] Jacobson, N.: Structure and Representations of Jordan Algebras. A.M.S. Colloquium Publications, Vol. XXXIX. Providence, Rhode Island: A.M.S. 1968 · Zbl 0218.17010
[7] Janssen, G.: Formal-reelle Jordanalgebren unendlicher Dimension und verallgemeinerte Positivitätsbereiche. J. Reine Angew. Math.249, 173-209 (1971) · Zbl 0219.17009
[8] Jordan, P., von Neumann, J., Wigner, E.: On an algebraic generalization of the quantum mechanical formalism. Ann. of Math.35, 29-64 (1934) · JFM 60.0902.02
[9] Kaup, W.: On the Automorphisms of Certain Symmetric Complex Manifolds of Infinite Dimensions. An. Acad. Brasil. Ci.48, 153-163 (1976) · Zbl 0376.32028
[10] Kaup, W.: Algebraic characterization of symmetric complex Banach manifolds. Math. Ann.228, 39-64 (1977) · Zbl 0344.58006
[11] Kaup, W., Upmeier, H.: An infinitesimal version of Cartan’s uniqueness theorem. Manuscripta Math.22, 381-401 (1977) · Zbl 0371.32021
[12] Kaup, W., Upmeier, H.: Jordan Algebras and Symmetric Siegel Domains in Banach Spaces. Math. Z.157, 179-200 (1977) · Zbl 0357.32018
[13] Koecher, M.: Jordan Algebras and their Applications. Lecture notes. Minneapolis: University of Minnesota 1962 · Zbl 0128.03101
[14] Koecher, M.: An Elementary Approach to Bounded Symmetric Domains. Houston, Texas: Rice University 1969 · Zbl 0217.10901
[15] Loos, O.: Bounded symmetric domains and Jordan Paris. Irvine, Calif.: University of California 1977
[16] Wright, J.D.M.: JordanC *-algebras. Michigan Math. J. (to appear)
[17] Wright, J.D.M., Youngson, M.A.: A Russo Dye Theorem for JordanC *-Algebras. Proceedings of a Conference in Functional Analysis (Paderborn 1977). Amsterdam-London: North Holland (to appear) · Zbl 0372.46060
[18] Wright, J.D.M., Youngson, M.A.: On Isometries of Jordan Algebras. Preprint · Zbl 0384.46041
[19] Youngson, M.A.: A Vidav Theorem for Banach Jordan Algebras. Preprint · Zbl 0392.46038
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.