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Jordan algebras and symmetric Siegel domains in Banach spaces. (English) Zbl 0357.32018
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
46B99Normed linear spaces and Banach spaces
17C99Jordan algebras (algebras, triples and pairs)
[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)