Keywords
- Banach Space
- Triple System
- Jordan Algebra
- Symmetric Part
- Triple Product
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References
Arazy, J., On biholomorphic automorphisms of the unit ball of unitary matrix spaces, Linear Algebra and its Applications, 80(1986), 180–182.
Arazy, J. and Friedman, Y., Contractive projections in C 1 and C ∞, Memoris of Amer. Math. Soc., 13 (1978), No. 200.
Barton, T., Bounded Reinhardt domains in complex Banach spaces, Ph.D. Thesis, Kent State University (1984).
Barton, T. Biholmorphic equivalence of bounded Reinhardt domains, An. Sci. Norm. Sup, Pisa (to appear).
Barton, T., Dineen, S. and Timoney, R., Bounded Reinhardt domains in Banach spaces, Compositio Mathematica (to appear).
Barton, T., and Timoney, R., Weak * continuity of Jordan triple products and applications, Math. Scand. (to appear).
Braun, R., Kaup, W. and Upmeier, H., On the automorphisms of circular and Reinhardt domains in complex Banach spaces, Manuscripta Math. 25 (1978), 97–133.
Cartan, E., Sur les domaines bornés homogènes de l'espace de n variables complexes, Abh. Math. Sem. Univ. Hamburg 11(1935), 116–162.
Cartan, H., Les fonctions delta de deux variables complexes et le problème de la représentation analytique, J. Math. Pures. Appl. 9e série, 10 (1931), 1–144.
Cartan, H., Sur les groupes de transformations analy tiques, Act. Sci. Indust., Exposés Math., 9, Hermann, Paris, 1935.
Dineen, S., Complex analysis in locally convex spaces, North Holland Math. Studies, 57, 1981.
Dineen, S., The second dual of a JB*-triple system. Complex analysis, functional analysis and approximation theory, J. Mujica (editor), North. Holland, Ud. 125, 1986.
Dineen, S., Complete holomorphic vector fields on the second dual of a Banach space, Math. Scand. (to appear).
Effros, E. and Størmer, E., Positive projections and Jordan structure in operator algebra, Math. Scand. 45 (1979), 127–138.
Franzoni, T. and Vesentini, E., Holomorphic maps and invariant distances, North Holland Math. Studies, 40, 1980.
Friedman, Y. and Russo, B., Contractive projections on operator triple systems, Math. Scand. 52 (1983), 279–311.
Friedman, Y. and Russo, B., Solution of the contractive projection problem, J. Funct. Anal. 60 (1985), 56–79.
Friedman, Y. and Russo, B., The Gelfand Naimark theorem for JB*-triples, Duke Math. J. (to appear).
Gohberg, I.C. and Krein, M.G., Introduction to the theory of linear non-self adjoint operators, Amer. Math. Soc. Translations, Vol. 18.
Harris, L., Bounded symmetric homogeneous domains in infinite dimensional spaces, Lecture notes in Math. 364, Springer-Verlag, New York-Heidelberg-Berlin, 1974, 13–40.
Harris, L., Schwarz Pick systems of pseudometries for domains in normed linear spaces, Advances in Holomorphy, J. A. Barroso (ed.), North Holland, 1979, 345–406.
Harris, L., A generalization of C*-algebras, Proc. London. Math. Soc. (3) 42 (1981), 331–361.
Isidro, J. M. and Stacho, L. L., Holomorphic automorphism groups in Banach spaces: an elementary introduction, North Holland Math. Studies, 105 (1985).
Isidro, J. M. and Vigué, J.P., Sur la topologie du groupes des automorphismes analytiques d'un domaine cercle borné, B.S.M.F. 106 (1982), 417–426.
Kalton, N. J. and Wood, G.V., Orthonormal systems in Banach spaces and their applications, Math. Proc. Camb. Phil. Soc. 79 (1976), 493–510.
Kaup, W., Algebraic characterization of symmetric complex Banach manifolds, Math. Ann. 228 (1977), 39–64.
Kaup, W., Jordan algebras and holomorphy, Functional analysis, holomorphy and approximation theory, Lecture Notes in Mathematics 843, Springer-Verlag, Berlin-Heidelberg-New York, 1981, 341–365.
Kaup, W., A Riemann mapping theorem for bounded symmetric domains in complex Banach spaces, Math. Z. 183 (1983) 503–529.
Kaup, W., Contractive projections on Jordan C*-algebras and generalizations, Math. Scand. 54 (1984), 95–100.
Kaup, W. and Upmeier, H., Banach spaces with biholomorphically equivalent unit balls are isomorphic, Proc. Amer. Math. Soc. 58 (1978), 129–133.
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces I. Ergebnisse 92, Springer-Verlag, New York-Heidelberg-Berlin, 1977.
Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II. Ergebnisse 97, Springer-Verlag, New York-Heidelberg-Berlin, 1979.
Loos, O., Bounded symmetric domains and Jordan pairs, Lecture Notes, University of California at Irvine, 1977.
Rosenthal, H., The Lie algebra of a Banach space, preprint.
Rosenthal, H., Functional Hilbertian sums, preprint.
Stacho, L. L., A short proof that the biholomorphic automorphisms of the unit ball of L p spaces are linear, Acta. Sci. Math. 41 (1979), 381–383.
Stacho, L. L., A projection principle concerning biholomorphic automorphisms, Acta. Sci. Math. 44 (1982), 99–124.
Sunada, T., Holomorphic equivalence problem for bounded Reinhardt domains, Math. Ann. 235 (1978), 111–128.
Thullen, P., Die Invarianz des Mittelpunktes von Kreiskörpern, Math. Ann. 104 (1931) 244–259.
Upmeier, H., Über die Automorphismengruppen beschränkter Gebiete in Banachräumen. Dissertation, Tübingen, 1975.
Upmeier, H., Über die Automorphismengruppen von Banach-Mannigfaltigkeiten mit invarianter Metrik, Math. Ann. 223 (1976), 279–288.
Upmeier, H., Symmetric Banach Manifolds and Jordan C*-algebras, North Holland Math. Studies, 104 (1985).
Upmeier, H., Jordan algebras in analysis, operator theory and quantum mechanics, CBMS-NSF Regional Conference, Irvine, 1985.
Vigué, J. P., Le groupe des automorphismes analytiques d'un domaine borné d'un espace de Banach complexe. Applications aux domaines bornés symétriques, Ann. Sci. Ec. Norn. Sup. 4e série 9 (1976), 203–282.
Vigué, J. P., Les domaines bornés symétriques d'un espace de Banach complexeet les systèmes triples de Jordan, Math. Ann. 229 (1977), 223–231.
Vigué, J. P., Automorphismes analytiques des produits de domaines bornés, Ann. Sci. Ec.Norm. Sup. 4e série 11 (1978), 229–246.
Vigué, J. P., Les automorphismes analytiques isométriques d'une variété complexe normée, Bull. Soc. Math. France 110 (1982), 49–73.
Vigué, J. P., Automorphismes analytiques d'un domaine de Reinhardt borné d'un espace de Banach à base, Ann. de l'Inst. Fourier (Grenoble), 34, 2 (1984), 67–87.
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Arazy, J. (1987). An application of infinite dimensional holomorphy to the geometry of banach spaces. In: Lindenstrauss, J., Milman, V.D. (eds) Geometrical Aspects of Functional Analysis. Lecture Notes in Mathematics, vol 1267. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078141
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DOI: https://doi.org/10.1007/BFb0078141
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