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Banach spaces with biholomorphically equivalent unit balls are isomorphic. (English) Zbl 0337.32012

MSC:
32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects)
46B99 Normed linear spaces and Banach spaces; Banach lattices
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
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[3] Lawrence A. Harris, Bounded symmetric homogeneous domains in infinite dimensional spaces, Proceedings on Infinite Dimensional Holomorphy (Internat. Conf., Univ. Kentucky, Lexington, Ky., 1973) Springer, Berlin, 1974, pp. 13 – 40. Lecture Notes in Math., Vol. 364. · Zbl 0293.46049
[4] Wilhelm Kaup, Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete, Manuscripta Math. 3 (1970), 257 – 270 (German, with English summary). · Zbl 0202.36504
[5] Wilhelm Kaup, On the automorphisms of certain symmetric complex manifolds of infinite dimensions, An. Acad. Brasil. Ci. 48 (1976), no. 2, 153 – 163. · Zbl 0376.32028
[6] Leopoldo Nachbin, Topology on spaces of holomorphic mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 47, Springer-Verlag New York Inc., New York, 1969. · Zbl 0258.46027
[7] Harald Upmeier, Über die Automorphismengruppen beschränkter Gebiete in Banachräumen, Mathematisches Institut, Universität Tübingen, Tübingen, 1975 (German). Dissertation zur Erlangung des Grades eines Doktors der Naturwissenschaften dem Fachbereich Mathematik der Eberhard-Karls-Universität zu Tübingen. · Zbl 0313.32039
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