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


MSC:

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
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References:

[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
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[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
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