bdim: Biblioteca Digitale Italiana di Matematica

Un progetto SIMAI e UMI

Referenza completa

Włodarczyk, Kazimierz:
The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of \( C^{*} \)-algebras (L'esistenza di derivate angolari di mappe olomorfe di domini di Siegel in una generalizzazione di algebre \( C^{*} \))
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni Serie 9 5 (1994), fasc. n.4, p. 309-328, (English)
pdf (1.71 MB), djvu (395 Kb). | MR1320583 | Zbl 0827.47030

Sunto

Questo articolo ha lo scopo di avviare uno studio sistematico dell'esistenza di limiti e derivate angolari di mappe olomorfe di domini di Siegel di dimensione infinita in algebre \( J^{*} \). Poiché le algebre \( J^{*} \) sono generalizzazioni naturali di algebre \( C^{*} \), algebre \( B^{*} \), algebre \( JC^{*} \), algebre ternarie e spazi di Hilbert complessi, ne seguono diversi risultati significativi. Vengono esaminati alcuni esempi.
Referenze Bibliografiche
[1] T. ANDO - KY FAN, Pick-Julia theorems for operators. Math. Z., 168, 1979, 23-34. | fulltext EuDML | fulltext (doi) | MR 542181 | Zbl 0389.47004
[2] R. B. BURCKEL, An Introduction to Classical Complex Analysis. Vol. I, Academic Press, New York-San Francisco 1979. | MR 555733 | Zbl 0434.30002
[3] C. CARATHÉODORY, Über die Winkelderivierten von beschränkten analytischen Functionen. Sitz. Ber. Preuss. Akad., Phys.-Math., IV, 1929, 1-18. | Jbk 55.0209.02
[4] C. CARATHÉODORY, Conformal Representations. Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge 1952. | Zbl 0047.07905
[5] C. CARATHÉODORY, Theory of Functions. Vol. 2, Chelsea Publishing Company, New York 1960. | Zbl 0056.06703
[6] E. CARTAN, Sur les domaines bornés homogènes de l'espace de \( n \) variables complexes. Abh. Math. Sem. Univ. Hamburg, 11, 1935, 116-162. | Zbl 0011.12302
[7] C. C. COWEN - CH. POMMERENKE, Inequalities for the angular derivative of an analytic function in the unit disk. J. London Math. Soc., (2), 26, 1982, 271-289. | fulltext (doi) | MR 675170 | Zbl 0476.30001
[8] S. DINEEN, The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford 1989. | MR 1033739 | Zbl 0708.46046
[9] B. G. EKE, On the angular derivative of regular functions. Math. Scand., 21, 1967, 122-127. | fulltext EuDML | MR 241617 | Zbl 0167.06301
[10] KY FAN, Iteration of analytic functions of operators. Math. Z., 179, 1982, 293-298. | fulltext EuDML | fulltext (doi) | MR 649033 | Zbl 0465.47017
[11] KY FAN, The angular derivative of an operator-valued analytic function. Pacific J. Math., 121, 1986, 67-72. | fulltext mini-dml | MR 815033 | Zbl 0588.47018
[12] T. FRANZONI - E. VESENTINI, Holomorphic Maps and Invariant Distances. North-Holland Mathematics Studies 40, Amsterdam-New York-Oxford 1980. | MR 563329 | Zbl 0447.46040
[13] J. L. GOLDBERG, Functions with positive real part in a half plane. Duke Math. J., 29, 1962, 333-339. | fulltext mini-dml | MR 164041 | Zbl 0101.29702
[14] L. A. HARRIS, Banach algebras with involution and Möbius transformations. J. Functional Anal., 11, 1972, 1-16. | MR 352994 | Zbl 0239.46058
[15] L. A. HARRIS, Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York 1974, 13-40. | MR 407330 | Zbl 0293.46049
[16] L. A. HARRIS, Operator Siegel domains. Proc. Roy. Soc. Edinburgh, 79 A, 1977, 137-156. | MR 484600 | Zbl 0376.32027
[17] L. A. HARRIS, A generalization of \( C^{*} \)-algebras. Proc. London Math. Soc., (3), 41, 1981, 331- 361. | fulltext (doi) | MR 607306 | Zbl 0476.46054
[18] L. A. HARRIS, Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147. | fulltext (doi) | MR 1160906 | Zbl 0760.47018
[19] L.-K. HUA, On the theory of automorphic functions of a matrix variable I - Geometrical Basis. Amer. J. Math., 66, 1944, 470-488. | MR 11133 | Zbl 0063.02919
[20] L.-K. HUA, On the theory of automorphic functions of a matrix variable II - The classification of hypercircles under the symplectic group. Amer. J. Math., 66, 1944, 531-563. | MR 11134 | Zbl 0063.02920
[21] W. KAUP, Algebraic characterization of symmetric complex Banach manifolds. Math. Ann., 228, 1977, 39-64. | fulltext EuDML | MR 454091 | Zbl 0335.58005
[22] W. KAUP, Bounded symmetric domains in complex Hilbert spaces. Symp. Math., Istituto Nazionale di Alta Matematica Francesco Severi, 26, 1982, 11-21. | MR 663020 | Zbl 0482.32012
[23] Y.-L. KIN, Inequalities for fixed points of holomorphic functions. Bull. London Math. Soc., 22, 1990, 446-452. | fulltext (doi) | MR 1082013 | Zbl 0725.30012
[24] M. KOECHER, An Elementary Approach to Bounded Symmetric Domain. Rice Univ., Houston, Texas 1969. | MR 261032 | Zbl 0217.10901
[25] A. KORANYI - J. WOLFF, Generalized Cayley transformations of bounded symmetric domains. Amer. J. Math., 87, 1965, 899-939. | MR 192002 | Zbl 0137.27403
[26] A. KORANYI - J. WOLFF, Realization of hermitian symmetric spaces as generalized half-planes. Ann. of Math., 81, 1965, 265-288. | MR 174787 | Zbl 0137.27402
[27] E. LANDAU - G. VALIRON, A deduction from Schwarzs lemma. J. London Math. Soc., 4, 1929, 162-163. | fulltext (doi) | MR 1575036 | Jbk 55.0769.02
[28] O. LOOS, Jordan triple systems, \( R \)-spaces and bounded symmetric domains. Bull. Amer. Math. Soc., 77, 1971, 558-561. | fulltext mini-dml | MR 281846 | Zbl 0228.32012
[29] O. LOOS, Bounded symmetric domains and Jordan pairs. Univ. of California, Irvine 1977.
[30] B. D. MACCLUER - J. H. SHAPIRO, Angular derivatives and compact composition operators on the Hardy and Bergman spaces. Canadian J. Math., 38, 1986, 878-906. | fulltext (doi) | MR 854144 | Zbl 0608.30050
[31] L. NACHBIN, Topology on Spaces of Holomorphic Mappings. Springer-Verlag, Berlin-Heidelberg-New York 1969. | MR 254579 | Zbl 0172.39902
[32] R. NEVANLINNA, Analytic Functions. Springer-Verlag, Berlin-Heidelberg-New York 1969. | MR 279280 | Zbl 0199.12501
[33] I. I. PJATETSKIJ-SHAPIRO, Automorphic Functions and the Geometry of Classical Domains. Gordon-Breach, New York 1969. | MR 252690 | Zbl 0196.09901
[34] CH. POMMERENKE, Univalent Functions. Vandehoeck and Ruprecht, Göttingen 1975. | MR 507768 | Zbl 0298.30014
[35] W. RUDIN, Function Theory in the Unit Ball of \( C^{n} \). Springer-Verlag, New York-Heidelberg-Berlin 1980. | MR 601594 | Zbl 1139.32001
[36] D. SARASON, Angular derivatives via Hilbert space. Complex Variables Theory Appl., 10, 1988, 1-10. | MR 946094 | Zbl 0635.30024
[37] J. H. SHAPIRO, Composition Operators and Classical Function Theory. Springer-Verlag, New York 1993. | MR 1237406 | Zbl 0791.30033
[38] H. UPMEIER, Symmetric Banach Manifolds and Jordan \( C^{*} \)-Algebras. North-Holland, Amsterdam, Math. Studies, vol. 104, 1985. | MR 776786 | Zbl 0561.46032
[39] H. UPMEIER, Jordan algebras in analysis, operator theory, and quantum mechanics. Regional Conference Series in Math., 67, Amer. Math. Soc., Providence, RI, 1987. | MR 874756 | Zbl 0608.17013
[40] G. VALIRON, Fonctions analytiques. Presses Univ. de France, Paris 1954. | MR 61658 | Zbl 0055.06702
[41] E. VESENTINI, Su un teorema di Wolff e Denjoy. Rend. Sem. Mat. Fis. Milano, LIII, 1983, 17-25. | fulltext (doi) | MR 858531 | Zbl 0596.30038
[42] E. WARSCHAWSKI, Remarks on the angular derivatives. Nagoya Math. J., 42, 1971, 19-32. | fulltext mini-dml | MR 274733 | Zbl 0209.11002
[43] K. WŁODARCZYK, On holomorphic maps in Banach spaces and \( J^{*} \)-algebras. Quart. J. Math. Oxford, (2), 36, 1985, 495-511. | fulltext (doi) | MR 816489 | Zbl 0595.46048
[44] K. WŁODARCZYK, Pick-Julia theorems for holomorphic maps in \( J^{*} \)-algebras and Hilbert spaces. J. Math. Anal. Appl., 120, 1986, 567-571. | fulltext (doi) | MR 864774 | Zbl 0612.46044
[45] K. WŁODARCZYK, Studies of iterations of holomorphic maps in \( J^{*} \)-algebras and complex Hilbert spaces. Quart. J. Math. Oxford, (2), 37, 1986, 245-256. | fulltext (doi) | MR 841432 | Zbl 0595.47046
[46] K. WŁODARCZYK, Julia's lemma and Wolff's theorem for \( J^{*} \)-algebras and complex Hilbert spaces. Proc. Amer. Math. Soc., 99, 1987, 472-476. | Zbl 0621.46041
[47] K. WŁODARCZYK, The angular derivative of Fréchet-holomorphic maps in \( J^{*} \)-algebras and complex Hilbert spaces. Proc. Kon. Nederl. Akad. Wetensch., A91, 1988, 455-468; Indag. Math., 50, 1988, 455-468. | MR 976528 | Zbl 0665.46034
[48] K. WŁODARCZYK, Hyperbolic geometry in bounded symmetric homogeneous domains of \( J^{*} \)-algebras. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 201-211. | MR 1111769 | Zbl 0744.46035
[49] K. WŁODARCZYK, The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces. Rend. Mat. Acc. Lincei., s. 9, 4, 1993, 171-179. | fulltext bdim | fulltext mini-dml | MR 1250495 | Zbl 0817.46048
[50] K. WŁODARCZYK, Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains. Rend. Mat. Acc. Lincei, s. 9, 5, 1994, 43-53. | fulltext bdim | MR 1273892 | Zbl 0802.46060

La collezione può essere raggiunta anche a partire da EuDML, la biblioteca digitale matematica europea, e da mini-DML, il progetto mini-DML sviluppato e mantenuto dalla cellula Math-Doc di Grenoble.

Per suggerimenti o per segnalare eventuali errori, scrivete a

logo MBACCon il contributo del Ministero per i Beni e le Attività Culturali