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Jordan algebras and symmetric Siegel domains in Banach spaces. (English) Zbl 0357.32018

MSC:
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
46B99 Normed linear spaces and Banach spaces; Banach lattices
17C99 Jordan algebras (algebras, triples and pairs)
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[1] Braun, H., Koecher, M.: Jordan-Algebren. Berlin-Heidelberg-New York: Springer 1966
[2] Harris, L.A.: Bounded symmetric homogeneous domains in infinite dimensional spaces. In: Proceedings on Infinite Dimensional Holomorphy (Lexington 1973) pp. 13-40. Lecture Notes in Mathematics364, Berlin-Heidelberg-New York: Springer 1973 · Zbl 0293.46049
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[9] Koecher, M.: An elementary approach to bounded symmetric domains. Rice Univ. 1969 · Zbl 0217.10901
[10] Korányi, A., Wolf, J.: Generalized Cayley transformations of bounded symmetric domains. Amer. J. Math.87, 899-939 (1965) · Zbl 0137.27403 · doi:10.2307/2373253
[11] Loos, O.: Jordan triple systems,R-spaces and bounded symmetric domains. Bull. Amer. Math. Soc.77, 558-561 (1971) · Zbl 0228.32012 · doi:10.1090/S0002-9904-1971-12753-2
[12] Loos, O.: Jordan pairs. Lecture Notes in Mathematics160, Berlin-Heidelberg-New York: Springer 1975 · Zbl 0301.17003
[13] McCrimmon, K.: Norms and noncommutative Jordan algebras. Pacific J. Math.15, 925-956 (1965) · Zbl 0139.25501
[14] Nakajima, K.: On realization of Siegel domains of the second kind as those of the third kind. J. Math. Kyoto Univ.16, 143-166 (1976) · Zbl 0344.32023
[15] Pjateckii-?apiro, I.I.: Automorphic functions and the geometry of classical domains. New York-London-Paris: Gordon and Breach 1969
[16] Sakai, S.:C *-Algebras andW *-Algebras. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0219.46042
[17] Satake, I.: Infinitesimal automorphisms of symmetric Siegel domains. Preprint
[18] Upmeier, H.: Über die Automorphismengruppen von Banachmannigfaltigkeiten mit invarianter Metrik. Math. Ann.223, 279-288 (1976) · Zbl 0326.58012 · doi:10.1007/BF01360959
[19] Vigué, J.-P.: Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Ann sci. École norm. sup., IV. Sér.9, 203-282 (1976)
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