On complex Banach manifolds similar to Stein manifolds

Imre Patyi

doi:10.1016/j.crma.2010.11.020

Complex Analysis/Analytic Geometry

On complex Banach manifolds similar to Stein manifolds

Presented by: Jean-Pierre Demailly

Imre Patyi ¹

¹ Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, USA

Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 43-45.

Abstract
Résumé

We give an abstract definition, similar to the axioms of a Stein manifold, of a class of complex Banach manifolds in such a way that a manifold belongs to the class if and only if it is biholomorphic to a closed split complex Banach submanifold of a separable Banach space.

On donne ici une définition d'une classe de variétés banachiques complexes analogues aux variétés de Stein par leur définition et leurs propriétés. On montre qu'une variété banachique quelconque de cette classe est biholomorphe à une sous-variété banachique complexe fermée et scindée dans un espace de Banach complexe séparable, et réciproquement, qu'une telle sous-variété est bien toujours membre de la classe.

Received: 2010-10-22
Accepted: 2010-11-19
Published online: 2010-12-18

DOI: 10.1016/j.crma.2010.11.020

Author's affiliations:

Imre Patyi ¹

¹ Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303-3083, USA

@article{CRMATH_2011__349_1-2_43_0,
     author = {Imre Patyi},
     title = {On complex {Banach} manifolds similar to {Stein} manifolds},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {43--45},
     publisher = {Elsevier},
     volume = {349},
     number = {1-2},
     year = {2011},
     doi = {10.1016/j.crma.2010.11.020},
     language = {en},
}

TY  - JOUR
AU  - Imre Patyi
TI  - On complex Banach manifolds similar to Stein manifolds
JO  - Comptes Rendus. Mathématique
PY  - 2011
SP  - 43
EP  - 45
VL  - 349
IS  - 1-2
PB  - Elsevier
DO  - 10.1016/j.crma.2010.11.020
LA  - en
ID  - CRMATH_2011__349_1-2_43_0
ER  -

%0 Journal Article
%A Imre Patyi
%T On complex Banach manifolds similar to Stein manifolds
%J Comptes Rendus. Mathématique
%D 2011
%P 43-45
%V 349
%N 1-2
%I Elsevier
%R 10.1016/j.crma.2010.11.020
%G en
%F CRMATH_2011__349_1-2_43_0

Imre Patyi. On complex Banach manifolds similar to Stein manifolds. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 43-45. doi : 10.1016/j.crma.2010.11.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.020/

References
Cited by

[1] L. Lempert Plurisubharmonic domination, J. Amer. Math. Soc., Volume 17 (2004), pp. 361-372

[2] L. Lempert; I. Patyi Analytic sheaves in Banach spaces, Ann. Sci. École Norm. Sup. Sér. 4, Volume 40 (2007), pp. 453-486

[3] I. Patyi, On holomorphic domination, I, , Bull. Sci. Math., , in press. | arXiv | DOI

Cited by Sources:

Comments - Policy