Analytic sheaves in Banach spaces
Annales scientifiques de l'École Normale Supérieure (2007)
- Volume: 40, Issue: 3, page 453-486
- ISSN: 0012-9593
Access Full Article
topHow to cite
topLempert, László, and Patyi, Imre. "Analytic sheaves in Banach spaces." Annales scientifiques de l'École Normale Supérieure 40.3 (2007): 453-486. <http://eudml.org/doc/82718>.
@article{Lempert2007,
author = {Lempert, László, Patyi, Imre},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {plain sheaves; plain homomorphisms; complete resolution; cohesive sheaf},
language = {eng},
number = {3},
pages = {453-486},
publisher = {Elsevier},
title = {Analytic sheaves in Banach spaces},
url = {http://eudml.org/doc/82718},
volume = {40},
year = {2007},
}
TY - JOUR
AU - Lempert, László
AU - Patyi, Imre
TI - Analytic sheaves in Banach spaces
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2007
PB - Elsevier
VL - 40
IS - 3
SP - 453
EP - 486
LA - eng
KW - plain sheaves; plain homomorphisms; complete resolution; cohesive sheaf
UR - http://eudml.org/doc/82718
ER -
References
top- [1] Bishop E., Analytic functions with values in a Fréchet space, Pacific J. Math.12 (1962) 1177-1192. Zbl0116.06301MR159037
- [2] Bredon G.E., Sheaf Theory, second ed., Springer, New York, 1997. Zbl0874.55001MR1481706
- [3] Bungart L., Holomorphic functions with values in locally convex spaces and applications to integral formulas, Trans Amer. Math. Soc.111 (1964) 317-344. Zbl0142.33902MR157004
- [4] Cartan H., Séminaire École Norm. Sup. 4, Fonctions analytiques de plusieurs variables complexes, Paris, 1951–52.
- [5] Dineen S., Bounding subsets of a Banach space, Math. Ann.192 (1971) 61-70. Zbl0202.12803MR303290
- [6] Docquier F., Grauert H., Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten, Math. Ann.140 (1960) 94-123. Zbl0095.28004MR148939
- [7] Douady A., Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Ann. Inst. Fourier (Grenoble)16 (1966) 1-95. Zbl0146.31103MR203082
- [8] Douady A., A remark on Banach analytic spaces, in: Symposium on Infinite-Dimensional Topology, Baton Rouge, LA, 1967, Ann. of Math. Studies, vol. 69, Princeton Univ. Press, Princeton, NJ, 1972, pp. 41-42. Zbl0229.54031MR404704
- [9] Griffiths P., Adams J., Topics in Algebraic and Analytic Geometry, Mathematical Notes, Princeton Univ. Press, Princeton, NJ, 1974. Zbl0302.14003MR355119
- [10] Josefson B., Bounding subsets of , J. Math. Pures Appl.57 (1978) 397-421. Zbl0403.46011MR524627
- [11] Josefson B., Approximations of holomorphic functions in certain Banach spaces, Internat. J. Math.15 (2004) 467-471. Zbl1061.46041MR2072089
- [12] Kelly G.M., Basic Concepts of Enriched Category Theory, Cambridge Univ. Press, Cambridge, 1982. Zbl0478.18005MR651714
- [13] Leiterer J., Banach coherent analytic Fréchet sheaves, Math. Nachr.85 (1978) 91-109. Zbl0409.32017MR517643
- [14] Lempert L., The Dolbeault complex in infinite dimensions I, J. Amer. Math. Soc.11 (1998) 485-520. Zbl0904.32014MR1603858
- [15] Lempert L., Approximation de fonctions holomorphes d'un nombre infini de variables, Ann. Inst. Fourier (Grenoble)49 (1999) 1293-1304. Zbl0944.46046MR1703089
- [16] Lempert L., Approximation of holomorphic functions of infinitely many variables II, Ann. Inst. Fourier (Grenoble)50 (2000) 423-442. Zbl0969.46032MR1775356
- [17] Lempert L., The Dolbeault complex in infinite dimensions III, Invent. Math.142 (2000) 579-603. Zbl0983.32010MR1804162
- [18] Lempert L., Plurisubharmonic domination, J. Amer. Math. Soc.17 (2004) 361-372. Zbl1042.32013MR2051614
- [19] Lempert L., Vanishing cohomology for holomorphic vector bundles in a Banach setting, Asian J. Math.8 (2004) 65-86. Zbl1089.32011MR2128298
- [20] Meylan F., Approximation of holomorphic functions in Banach spaces admitting a Schauder decomposition, Ann. Scuola Norm. Sup. Pisa (2006). Zbl1150.46017MR2240163
- [21] Mujica J., Complex Analysis in Banach Spaces, North-Holland, Amsterdam, 1986. Zbl0586.46040MR842435
- [22] Patyi I., On the equation in a Banach space, Bull. Soc. Math. France128 (2000) 391-406. Zbl0967.32036MR1792475
- [23] Patyi I., On the Oka principle in a Banach space, I, Math. Ann.326 (2003) 417-441. Zbl1044.32018MR1992271
- [24] Patyi I., On the Oka principle in a Banach space, II, Math. Ann.326 (2003) 443-458. Zbl1045.32023MR1992271
- [25] Patyi I., Cohomological characterization of pseudoconvexity in a Banach space, Math. Z.245 (2003) 371-386. Zbl1040.32028MR2013505
- [26] Patyi I., Analytic cohomology of complete intersections in a Banach space, Ann. Inst. Fourier (Grenoble)54 (2004) 147-158. Zbl1080.32017MR2069124
- [27] Patyi I., On holomorphic Banach vector bundles over Banach spaces, manuscript, math.CV/0509557.
- [28] Patyi I., An analytic Koszul complex in a Banach space, manuscript, math.CV/0509556.
- [29] Patyi I., Analytic cohomology in a Banach space, manuscript, math.CV/0507520.
- [30] Pestov V., Analytic subsets of Hilbert spaces, in: Fruchard A., Troesch A. (Eds.), Actes du colloque trajectorien, IRMA, Strasbourg, 1995, pp. 75-80. MR1369104
- [31] Ramis J.P., Sous-ensembles analytiques d'une variété banachique complexe, Springer, Berlin–New York, 1970. Zbl0212.42802
- [32] Serre J.-P., Faisceaux algébriques cohérents, Ann. Math.61 (1955) 197-278. Zbl0067.16201MR68874
- [33] Singer I., Bases in Banach Spaces, I–II, Springer, Berlin, 1981. Zbl0198.16601
- [34] Siu Y.T., Every Stein variety admits a Stein neighborhood, Invent. Math.38 (1976/77) 89-100. Zbl0343.32014MR435447
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.