×

zbMATH — the first resource for mathematics

On the automorphisms of circular and Reinhardt domains in complex Banach spaces. (English) Zbl 0398.32001

MSC:
32A07 Special domains in \({\mathbb C}^n\) (Reinhardt, Hartogs, circular, tube) (MSC2010)
46B20 Geometry and structure of normed linear spaces
32K05 Banach analytic manifolds and spaces
32A35 \(H^p\)-spaces, Nevanlinna spaces of functions in several complex variables
PDF BibTeX XML Cite
Full Text: DOI EuDML
References:
[1] BEHNKE,H., THULLEN,P.: Theorie der Funktionen mehrerer komplexer Veränderlichen. Berlin-Heidelberg-New York: Springer 1970 · Zbl 0204.39502
[2] BONSALL,F.F., DUNCAN,J.: Complete normed algebras. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0271.46039
[3] CARTAN,H.: Sur les groupes de transformations analytiques. Act.Sci.Ind. 198. Paris: Hermann 1935 · JFM 61.0370.02
[4] CARTAN,H.: Sur les fonctions de n variables complexes: Les transformations du produit topologique de deux domaines bornés. Bull.Soc.Math.France64, 37-48 (1936) · Zbl 0014.40804
[5] DAY,M.M.: Normed linear spaces. 3rd edition. Berlin-Heidelberg-New York: Springer 1973 · Zbl 0268.46013
[6] DUNKL,C., RAMIREZ,D.E.: Topics in harmonic analysis. New York: Appleton-Century-Crofts 1971 · Zbl 0227.43001
[7] DUREN,P.L.: Theory of Hp-spaces. New York and London: Academic Press 1970 · Zbl 0215.20203
[8] FORELLI,F.: The isometries of Hp. Can. J. Math.16, 721-728 (1964) · Zbl 0132.09403
[9] HARRIS,L.A.: Bounded symmetric homogeneous domains in infinite dimensional spaces. In: Lect.Notes in Math. 364. Berlin-Heidelberg-New York: Springer 1974 · Zbl 0293.46049
[10] HOFFMAN,K.: Banach spaces of analytic functions. Englewood Cliffs, N. J.: Prentice Hall 1962 · Zbl 0117.34001
[11] JOHNSON,B.E.: Continuity of derivations on commutative algebras. Amer.J.Math.91, 1-10 (1969) · Zbl 0181.41103
[12] KAUP,W.: Über das Randverhalten von holomorphen Automorphismen beschränkter Gebiete. Manuscripta math.3, 257-270 (1970) · Zbl 0202.36504
[13] KAUP,W.: Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen. Inventiones math.3, 43-70 (1967) · Zbl 0157.13401
[14] KAUP,W.: Algebraic characterization of symmetric complex Banach manifolds. Math.Ann.228, 39-64 (1977) · Zbl 0344.58006
[15] KAUP,W.: On the automorphisms of certain symmetric complex manifolds of infinite dimension. Anais. brasil.Ciênc.48 (2), 153-163 (1976) · Zbl 0376.32028
[16] KAUP,W.: Bounded symmetric domains in finite and infinite dimensions-a review. To appear in: Proceedings of a seminar on Several Complex Variables. Cortona (Italy) July 1977 · Zbl 0418.32020
[17] KAUP,W.,UPMEIER,H.: Banach spaces with biholomorphically equivalent unit balls are isomorphic. Proc.Amer.Math.Soc.58, 129-133 (1976) · Zbl 0337.32012
[18] KAUP,W., UPMEIER,H.: An infinitesimal version of Cartan’s uniqueness theorem. Manuscripta math.22, 381-401 (1977) · Zbl 0371.32021
[19] KAUP,W., UPMEIER,H.: Jordan algebras and symmetric Siegel domains in Banach spaces. Math.Z.157, 179-200 (1977) · Zbl 0357.32018
[20] PETERS,K.: Starrheitssätze für Produkte normierter Vektorräume endlicher Dimension und für Produkte hyperbolischer komplexer Räume. Math.Ann.208, 343-354 (1977) · Zbl 0281.32018
[21] RUDIN,W.: Lp-isometries and equimeasurability. Ind.U.Math.J.25, 215-227 (1976) · Zbl 0326.46011
[22] SCHOTTENLOHER,M.: Riemann domains: Basic results and open problems. In: Lecture Notes in Math. 364: Berlin-Heidelberg-New York: Springer 1974 · Zbl 0281.32022
[23] SUNADA,T.: Holomorphic equivalence problem for bounded Reinhardt domains. Math.Ann. To appear. · Zbl 0357.32001
[24] THORP,E., WHITLEY,R.: The strong maximum modulus theorem for analytic functions into a Banach space. Proc.Amer.Math.Soc.18, 640-646 (1967) · Zbl 0185.20102
[25] THULLEN,P.: Die Invarianz des Mittelpunktes von Kreiskörpern. Math.Ann.104, 244-259 (1931) · Zbl 0001.02303
[26] UPMEIER,H.: Über die Automorphismengruppen von Banach-Mannigfaltigkeiten mit invarianter Metrik. Math.Ann.223, 279-288 (1976) · Zbl 0326.58012
[27] VESENTINI,E.: On the automorphisms of balls. To appear in: Proceedings of a seminar on Several Complex Variables. Cortona (Italy) July 1977
[28] VIGUÉ,J.-P.: Le groupe des automorphismes analytiques d’un domaine borné d’un espace de Banach complexe. Application aux domaines bornés symétriques. Ann. scient. Éc. Norm. Sup, 4esérie,9, 203-282 (1976)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.