no. 4
Bounded analytic sets in Banach spaces
Annales de l'Institut Fourier, Tome 36 (1986) no. 4, pp. 229-243

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.

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.

@article{AIF_1986__36_4_229_0,
     author = {Aurich, Volker},
     title = {Bounded analytic sets in {Banach} spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {229--243},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {36},
     number = {4},
     year = {1986},
     doi = {10.5802/aif.1075},
     zbl = {0591.46005},
     mrnumber = {88h:32021},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1075/}
}
TY  - JOUR
AU  - Aurich, Volker
TI  - Bounded analytic sets in Banach spaces
JO  - Annales de l'Institut Fourier
PY  - 1986
SP  - 229
EP  - 243
VL  - 36
IS  - 4
PB  - Institut Fourier
PP  - Grenoble
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1075/
DO  - 10.5802/aif.1075
LA  - en
ID  - AIF_1986__36_4_229_0
ER  - 
%0 Journal Article
%A Aurich, Volker
%T Bounded analytic sets in Banach spaces
%J Annales de l'Institut Fourier
%D 1986
%P 229-243
%V 36
%N 4
%I Institut Fourier
%C Grenoble
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1075/
%R 10.5802/aif.1075
%G en
%F AIF_1986__36_4_229_0
Aurich, Volker. Bounded analytic sets in Banach spaces. Annales de l'Institut Fourier, Tome 36 (1986) no. 4, pp. 229-243. doi: 10.5802/aif.1075

[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. | Zbl | MR

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

[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. | Zbl | MR

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

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

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

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

[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. | Zbl | MR

[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. | Zbl | MR | EuDML

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

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

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

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

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

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

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

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

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

Cité par Sources :