The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces
Włodarczyk, Kazimierz
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993), p. 171-179 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

A classical Julia-Carathéodory theorem concerning radial limits of holomorphic maps in one dimension is extended to hyperbolic contractions of bounded symmetric domains in J*-algebras.

Un classico risultato di Julia e Carathéodory, relativo a limiti radiali di funzioni olomorfe di una variabile, viene esteso alle contrazioni iperboliche in domini limitati simmetrici in algebra J*.

Publié le : 1993-09-01
@article{RLIN_1993_9_4_3_171_0,
     author = {Kazimierz W\l odarczyk},
     title = {The Julia-Carath\'eodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {4},
     year = {1993},
     pages = {171-179},
     zbl = {0817.46048},
     mrnumber = {1250495},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1993_9_4_3_171_0}
}

Włodarczyk, Kazimierz. The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 4 (1993) pp. 171-179. http://gdmltest.u-ga.fr/item/RLIN_1993_9_4_3_171_0/

[1] Abate, M., Iteration theory, compactly divergent sequences and commuting holomorphic maps. Ann. Scuola Norm. Sup. Pisa, 18, 1991, 167-191. | MR 1129300 | Zbl 0760.32014

[2] Ando, T. - Fan, K., Pick-Julia theorems for operators. Math. Z., 168, 1979, 23-34. | MR 542181 | Zbl 0389.47004

[3] Beardon, A. F., Iteration of contractions and analytic maps. J. London Math. Soc, 41, 1990, 141-150. | MR 1063551 | Zbl 0662.30017

[4] Caratheodory, C., Conformal Representations. Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge1952. | MR 46435 | Zbl 0047.07905

[5] Cartan, E., Sur les domaines bornés homogènes de l'espace de n variables complexes. Abh. Math. Sem. Univ. Hamburg, 11, 1935, 116-162. | Zbl 0011.12302

[6] Chen, G.-N., Iteration for holomorphic maps of the open unit ball and the generalized upper half plane of Cn. J. Math. Anal. Appl., 98, 1984, 305-313. | MR 730507 | Zbl 0587.32008

[7] Dineen, S., The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford1989. | MR 1033739 | Zbl 0708.46046

[8] Dineen, S. - Timoney, R. - Vigue, J. P., Pseudodistances invariantes les domaines d'un espace localement convexe. Ann. Scuola Norm. Sup. Pisa, (4), 12, 1985, 515-529. | MR 848840 | Zbl 0603.46052

[9] Fan, K., Analytic functions of an operator contraction. Math. Z., 160, 1978, 275-290. | MR 482310 | Zbl 0441.30060

[10] Fan, K., Julia's lemma for operators. Math. Ann., 239, 1979, 241-245. | MR 522782 | Zbl 0378.47004

[11] Fan, K., Iteration of analytic functions of operators. Math. Z., 179, 1982, 293-298. | MR 649033 | Zbl 0465.47017

[12] Fan, K., The angular derivative of an operator-valued analytic function. Pacific J. Math., 121, 1986, 67-72. | MR 815033 | Zbl 0588.47018

[13] Franzoni, T. - Vesentini, E., Holomorphic Maps and Invariant Distance. North Holland, Amsterdam 1980. | MR 563329 | Zbl 0447.46040

[14] Harris, L. A., Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces. Lecture Notes in Mathematics, No. 364, Springer-Verlag, Berlin-Heidelberg-New York1974, 13-40. | MR 407330 | Zbl 0293.46049

[15] Harris, L. A., Schwarz-Pick systems of pseudometrics for domains in normed linear spaces. In: J. A. Barroso (ed.), Advances in Holomorphy. North Holland, Amsterdam 1979, 345-406. | MR 520667 | Zbl 0409.46053

[16] Harris, L. A., Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147, | MR 1160906 | Zbl 0760.47018

[17] Hervé, M., Analyticity in Infinite Dimensional Spaces. Walter de Gruyter, Berlin-New York1989. | MR 986066 | Zbl 0666.58008

[18] Kubota, Y., Iteration of holomorphic maps of the unit ball into itself. Proc. Amer. Math. Soc., 88, 1983, 476-480. | MR 699417 | Zbl 0518.32016

[19] Mac Cluer, B. D., Iterates of holomorphic self maps of the unit hall in CN. Michigan Math. J., 30, 1983, 97-106. | MR 694933 | Zbl 0528.32019

[20] Vesentini, E., Invariant distances and invariant differential metric in locally convex spaces. In: Spectral Theory. Polish Scientific Publishers, Warsaw1982, 493-512. | MR 738313 | Zbl 0505.32020

[21] Vesentini, E., Su un teorema di Wolff e Denjoy. Rend. Sem. Mat. Fis. Milano, LIII, 1983, 17-25. | MR 858531 | Zbl 0596.30038

[22] Wlodarczyk, K., Some properties of analytic maps of operators in J*-algebras. Monatsh. Math., 96, 1983, 325-330. | MR 729044 | Zbl 0521.46046

[23] Wlodarczyk, K., Studies of iterations of holomorphic maps in J*-algebras and complex Hilbert spaces. Quart. J. Math. Oxford, 37, 1986, 245-256. | MR 841432 | Zbl 0595.47046