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Jordan algebras and symmetric Siegel domains in Banach spaces. (English) Zbl 0357.32018
MSC:
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
46B99Normed linear spaces and Banach spaces
17C99Jordan algebras (algebras, triples and pairs)
References:
[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
[3]Harris, L.A.: Operator Siegel domains. Proc. roy. Soc. Edinburgh, Ser. A. To appear
[4]Harris, L.A., Kaup, W.: Linear algebraic groups in infinite dimensions. Illinois J. Math. In press.
[5]Janssen, G.: Formal-reelle Jordanalgebren unendlicher Dimension und verallgemeinerte Positivitätsbereiche. J. reine angew. Math.249, 173-200 (1971) · Zbl 0219.17009 · doi:10.1515/crll.1971.249.173
[6]Kaup, W.: Über die Automorphismen Graßmannscher Mannigfaltigkeiten unendlicher Dimension. Math. Z.144, 75-96 (1975) · Zbl 0322.32014 · doi:10.1007/BF01190938
[7]Kaup, W.: Algebraic characterization of symmetric complex Banach manifolds. Math. Ann.228, 39-64 (1977) · Zbl 0344.58006 · doi:10.1007/BF01360772
[8]Kaup, W., Upmeier, H.: An infinitesimal version of Cartan’s uniqueness theorem. Manuscripta math.22, 381-401 (1977) · Zbl 0371.32021 · doi:10.1007/BF01168224
[9]Koecher, M.: An elementary approach to bounded symmetric domains. Rice Univ. 1969
[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
[13]McCrimmon, K.: Norms and noncommutative Jordan algebras. Pacific J. Math.15, 925-956 (1965)
[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)
[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
[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)