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Algebraic characterization of symmetric complex Banach manifolds. (English) Zbl 0335.58005

MSC:
58B20 Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
47B15 Hermitian and normal operators (spectral measures, functional calculus, etc.)
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[1] Bonsall, F.F., Duncan, J.: Numerical ranges of operators on normed spaces and of elements of normed algebras. Cambridge: Cambridge University Press 1971 · Zbl 0207.44802
[2] Bourbaki, N.: Variétés differentielles et analytiques. Paragraphes 1 à 7. Paris: Hermann 1971 · Zbl 0206.50402
[3] Bourbaki, N.: Eléments de mathématique, groupes et algèbres de Lie. Paris: Hermann 1972 · Zbl 0244.22007
[4] Cartan, E.: Sur les domaines bornés homogènes de l’espace den variables complexes. Abh. Math. Sem. Univ. Hamburg11, 116-162 (1935) · Zbl 0011.12302 · doi:10.1007/BF02940719
[5] Cartan, H.: Sur les groupes de transformations analytiques. Actualités scient. et industr. Nr.198. Paris: Hermann 1935
[6] Douady, A.: Le problème des modules pour les sous-espaces analytiques compacts d’un espace analytique donné. Ann. Inst. Fourier16, 1-95 (1966) · Zbl 0146.31103
[7] Greenfield, S., Wallach, N.: Automorphism groups of bounded domains in Banach spaces. Trans. AMS166, 45-57 (1972) · Zbl 0254.32026 · doi:10.1090/S0002-9947-1972-0296359-6
[8] de la Harpe, P.: Classical Banach-Lie algebras and Banach-Lie groups of operators in Hilbert space. Lecture Notes in Mathematics285. Berlin, Heidelberg, New York: Springer 1972 · Zbl 0256.22015
[9] Harris, L.A.: Bounded symmetric homogeneous domains in infinite dimensional spaces. In: Proceedings on infinite dimensional holomorphy. Lecture Notes in Mathematics364. Berlin, Heidelberg, New York: Springer 1974 · Zbl 0293.46049
[10] Harris, L.A.: Operator-theoretic Siegel domains. In preparation · Zbl 0376.32027
[11] Harris, L.A., Kaup, W.: Linear algebraic groups in infinite dimensions. To appear in: Illinois J. Math. · Zbl 0385.22011
[12] Helgason, S.: Differential geometry and symmetric spaces. New York: Academic Press 1962 · Zbl 0111.18101
[13] Kaup, W.: Einige Bemerkungen über polynomiale Vektorfelder, Jordanalgebren und die Automorphismen von Siegelschen Gebieten. Math. Ann.204, 131-144 (1973) · Zbl 0252.22022 · doi:10.1007/BF01433410
[14] Kaup, W.: Über die Automorphismen Graßmannscher Mannigfaltigkeiten unendlicher Dimension. Math. Z.144, 75-96 (1975) · Zbl 0322.32014 · doi:10.1007/BF01190938
[15] Kaup, W.: On the automorphisms of certain symmetric complex manifolds of infinite dimension. To appear in: Anais da Academia Brasileira Ciências
[16] Kaup, W., Upmeier, H.: Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proceedings of the AMS58, 129-133 (1976) · Zbl 0337.32012 · doi:10.1090/S0002-9939-1976-0422704-3
[17] Koecher, M.: Gruppen und Lie-Algebren von rationalen Funktionen. Math. Z.109, 349-392 (1969) · Zbl 0181.04503 · doi:10.1007/BF01110558
[18] Koecher, M.: An elementary approach to bounded symmetric domains. Lecture Notes, Rice University, Houston 1969 · Zbl 0217.10901
[19] Korányi, A., Wolf, J.: Realization of hermitian symmetric space as generalized half-planes. Ann. of Math.81, 265-288 (1965) · Zbl 0137.27402 · doi:10.2307/1970616
[20] Lang, S.: Analysis II, Reading: Addison-Wesley 1969 · Zbl 0176.00504
[21] 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
[22] Loos, O.: Spiegelungsräume und homogene symmetrische Räume. Math. Z.99, 141-170 (1969) · Zbl 0148.17403 · doi:10.1007/BF01123745
[23] Loos, O.: Symmetric Spaces I. New York: Benjamin 1969 · Zbl 0175.48601
[24] Loos, O.: Jordan Pairs. Lecture Notes in Mathematics460. Berlin, Heidelberg, New York: Springer 1975 · Zbl 0301.17003
[25] Loos, O.: Bounded symmetric domains and Jordan triple systems I. Preprint · Zbl 0228.32012
[26] Loos, O., McCrimmon, K.: Speciality of Jordan triple systems. Preprint · Zbl 0362.17012
[27] Meyberg, K.: Jordan-Tripelsysteme und die Koecher-Konstruktion von Lie-Algebren. Math. Z.115, 58-78 (1970) · Zbl 0191.03003 · doi:10.1007/BF01109749
[28] Phillips, R.S.: On symplectic mappings of contraction operators. Studia Math.31, 15-27 (1968) · Zbl 0167.13501
[29] Satake, I.:Q-forms of symmetric domains and Jordan triple systems. Preprint · Zbl 0379.32026
[30] Upmeier, H.: Über die Automorphismen-Gruppen beschränkter Gebiete in Banachräumen. Dissertation Tübingen 1975 · Zbl 0313.32039
[31] Vigué, J.P.: Sur le groupe des automorphismes analytiques d’un ouvert borné d’un espace de Banach complexe. C.R. Acad. Sc. Paris:278, 617-620 (1974) and282, 111-114 (1976) · Zbl 0277.32020
[32] Vigué, J.P.: Les domaines bornés symmétriques d’un espace de Banach complexe. C.R. Acad. Sc. Paris:282, 211-213 (1976)
[33] Wolf, J.: Fine structure of hermitian symmetric spaces. Symmetric spaces, 271-288 (1965). New York: Marcel Dekker 1972 · Zbl 0137.27402
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