Bounded analytic sets in Banach spaces
Aurich, Volker
Annales de l'Institut Fourier, Tome 36 (1986), p. 229-243 / Harvested from Numdam

Des conditions sont présentées pour qu’un espace analytique X soit ou ne soit pas isomorphe à un sous-ensemble analytique fermé et borné d’un espace de Banach. Elles comprennent d’une part la propriété de Radon-Nikodym et d’autre part la métrique de Caratheodory.

Conditions are given which enable or disable a complex space X to be mapped biholomorphically onto a bounded closed analytic subset of a Banach space. They involve on the one hand the Radon-Nikodym property and on the other hand the completeness of the Caratheodory metric of X.

@article{AIF_1986__36_4_229_0,
     author = {Aurich, Volker},
     title = {Bounded analytic sets in Banach spaces},
     journal = {Annales de l'Institut Fourier},
     volume = {36},
     year = {1986},
     pages = {229-243},
     doi = {10.5802/aif.1075},
     mrnumber = {88h:32021},
     zbl = {0591.46005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_1986__36_4_229_0}
}
Aurich, Volker. Bounded analytic sets in Banach spaces. Annales de l'Institut Fourier, Tome 36 (1986) pp. 229-243. doi : 10.5802/aif.1075. http://gdmltest.u-ga.fr/item/AIF_1986__36_4_229_0/

[1] V. Aurich, Bifurcation of the solutions of holomorphic Fredholm equations and complex analytic graph theorems, Nonlinear Analysis, Theory, Methods et Applications, 6 (1982), 599-613. | MR 83m:58018 | Zbl 0487.58006

[2] V. Aurich, Bounded holomorphic embeddings of the unit disk into Banach spaces, Manuscripta Math., 45 (1983), 61-67. | MR 85b:58012 | Zbl 0525.46014

[3] V. Aurich, Über die Lösungsmengen analytischer semi-Fredholmscher Gleichungen, Habilitationsschrift, München, 1983.

[4] L. Bungart, Holomorphic functions with values in locally convex spaces and applications to integral formulas, Trans. Amer. Soc., 111 (1964), 317-344. | MR 28 #245 | Zbl 0142.33902

[5] D. Burghela, N. Kuiper, Hilbert manifolds, Ann. Math., 90 (1969), 379-417. | MR 40 #6589 | Zbl 0195.53501

[6] J. Diestel, J. J. Uhl Jr., Vector measures, Math. Surveys, 15, Amer. Math. Soc. (1977). | Zbl 0369.46039

[7] A. Douady, A remark on Banach analytic spaces. Symp. Infinite Dimens. Top., Ann. Math. Stud., 69 (1972), 41-42. | MR 53 #8504 | Zbl 0229.54031

[8] T. Franzoni, E. Vesentini, Holomorphic maps and invariant distances, Math. Stud., 40, North Holland, 1980. | MR 82a:32032 | Zbl 0447.46040

[9] L. A. Harris, Schwarz-Pick systems of pseudometrics for domains in normed linear spaces, Adv. in Holom., Ed.: J. A. Barroso, North Holland, 1979. | MR 80j:32043 | Zbl 0409.46053

[10] W. Hensgen, Die Michael-Vermutung und verwandte Fragestellungen, Diplomarbeit, München, 1981.

[11] R. E. Huff, P. D. Morris, Geometric characterizations of the Radon-Nikodym property in Banach spaces, Stud. Math., 56 (1976), 157-164. | MR 54 #897 | Zbl 0351.46011

[12] W. Kaup, Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen, Invent. Math., 3 (1967), 43-70. | MR 35 #6865 | Zbl 0157.13401

[13] S. Kobayashi, Hyperbolic manifolds and holomorphic mappings, M. Dekker Inc., New York, 1970. | MR 43 #3503 | Zbl 0207.37902

[14] A. Nagel, W. Rudin, Moebius-invariant function spaces on balls and spheres, Duke Math. J., 43 (1976), 841-865. | MR 54 #13135 | Zbl 0343.32017

[15] J. P. Ramis, Sous-ensembles analytiques d'une variété banachique complexe, Ergeb. der Math., 53, Springer, 1970. | MR 45 #2205 | Zbl 0212.42802

[16] W. Rudin, Function theory in the unit ball of Cn, Grundlehren, 241, Springer 1980. | MR 82i:32002 | Zbl 0495.32001

[17] M. Schottenloher, Embedding of Stein 'spaces into sequence spaces, Manuscripta math., 39 (1982), 15-29. | MR 84f:32017 | Zbl 0477.32014

[18] M. Schottenloher, Michael problem and algebras of holomorphic functions, Archiv der Math., 37 (1981), 241-247. | MR 83b:46061 | Zbl 0471.46036

[19] N. Sibony, Prolongement des fonctions holomorphes bornées et métrique de Carathéodory, Invent. Math., 29 (1975), 231-238. | MR 52 #6029 | Zbl 0333.32011

[20] S. Smale, An infinite dimensional version of Sard's theorem, Amer. J. of Math., 87 (1965), 861-866. | MR 32 #3067 | Zbl 0143.35301