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A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces. (English) Zbl 0519.32024

MSC:
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
17C65Jordan structures on Banach spaces and algebras
32K05Banach analytic spaces
32H99Holomorphic mappings on analytic spaces
References:
[1]Bonsall, F.F., Duncan, J.: Numerical ranges of operators on normed spaces and of elements of normed algebras. Cambridge: Cambridge University Press 1971
[2]Braun, H., Koecher, M.: Jordan-Algebren. Berlin-Heidelberg-New York: Springer 1966
[3]Braun, R., Kaup, W., Upmeier, H.: A holomorphic characterization of JordanC *-algebras. Math. Z.161, 277-290 (1978) · Zbl 0385.32002 · doi:10.1007/BF01214510
[4]Harris, L.A.: Bounded symmetric homogeneous domains in infinite dimensional spaces. In: Proceedings on infinite dimensional Holomorphy (Kentucky 1973); pp. 13-40. Lecture Notes in Math.364. Berlin-Heidelberg-New York: Springer 1974
[5]Harris, L.A., Kaup, W.: Linear algebraic groups in infinite dimensions. Illinois J. Math.21, 666-674 (1977)
[6]Jacobson, N.: Structure and representations of Jordan algebras. Amer. Math. Soc. Colloq. Publ.39. Providence: Amer. Math. Soc. 1968
[7]Kaup, W.: Algebraic characterization of symmetric complex manifolds. Math. Ann.228, 39-64 (1977) · Zbl 0344.58006 · doi:10.1007/BF01360772
[8]Kaup, W.: Über die Klassifikation der symmetrischen hermiteschen Mannigfaltigkeiten unendlicher Dimension I, Math. Ann.257, 463-483 (1981); II, Math. Ann.262, 57-75 (1983) · Zbl 0482.32010 · doi:10.1007/BF01465868
[9]Kaup, W.: Über die Automorphismen Graßmannscher Mannigfaltigkeiten unendlicher Dimension. Math. Z.144, 75-96 (1975) · Zbl 0322.32014 · doi:10.1007/BF01190938
[10]Koecher, M.: An elementary approach to bounded symmetric domains. In: Proceedings of a Conference on Complex Analysis (Houston 1969). Houston: Rice University 1969
[11]Koecher, M.: Gruppen und Lie-Algebren von rationalen Funktionen. Math. Z.109, 349-392 (1969) · Zbl 0181.04503 · doi:10.1007/BF01110558
[12]Loos, O.: Bounded symmetric domains and Jordan pairs. Mathematical Lectures. Irvine: University of California at Irvine 1977
[13]Loos, O.: Jordan pairs. Lecture notes in Math.460. Berlin-Heidelberg-New York: Springer 1975
[14]Loos, O.: Homogeneous algebraic varieties defined by Jordan pairs. Monatsh. Math.86, 107-129 (1978) · Zbl 0404.14020 · doi:10.1007/BF01320204
[15]Moreno, J.M.: JV-algebras. Math. Proc. Cambridge Philos. Soc.87, 47-50 (1980) · Zbl 0425.46037 · doi:10.1017/S0305004100056504
[16]Potapov, V.P.: The multiplicative structure ofJ-contractive matrix-functions. Amer. Math. Soc. Transl.15, 131-243 (1960)
[17]Upmeier, H.: Über die Automorphismengruppen von Banachmannigfaltigkeiten mit invarianter Metrik. Math. Ann.223, 279-288 (1976) · Zbl 0326.58012 · doi:10.1007/BF01360959
[18]Vigué, J.P.: Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Ann. Sci. École Norm. Sup. (4)9, 203-282 (1976)
[19]Vigué, J.P.: Sur la convexité des domaines bornés cerclés homogènes. Seminaire Lelong-Skoda. Lecture Notes in Math.822, pp. 317-331. Berlin-Heidelberg-New York: Springer 1980
[20]Wolf, J.: Fine structure of hermitian symmetric spaces. Symmetric spaces, pp. 271-357. New York: Decker 1972
[21]Wright, J.D.M.: JordanC *-algebras. Michigan Math. J.24, 291-302 (1977) · Zbl 0384.46040 · doi:10.1307/mmj/1029001946
[22]Youngson, M.A.: Non-unital Banach Jordan algebras andC *-triple systems. Proc. Edinburgh Math. Soc.24, 19-29 (1979) · Zbl 0451.46033 · doi:10.1017/S0013091500003965