The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of -algebras
- Volume: 5, Issue: 4, page 309-328
- ISSN: 1120-6330
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top- ANDO, T. - FAN, KY, Pick-Julia theorems for operators. Math. Z., 168, 1979, 23-34. Zbl0389.47004MR542181DOI10.1007/BF01214433
- BURCKEL, R. B., An Introduction to Classical Complex Analysis. Vol. I, Academic Press, New York-San Francisco1979. Zbl0434.30002MR555733
- CARATHÉODORY, C., Über die Winkelderivierten von beschränkten analytischen Functionen. Sitz. Ber. Preuss. Akad., Phys.-Math., IV, 1929, 1-18. JFM55.0209.02
- CARATHÉODORY, C., Conformal Representations. Cambridge Tracts in Mathematics and Mathematical Physics, Cambridge1952. Zbl0047.07905
- CARATHÉODORY, C., Theory of Functions. Vol. 2, Chelsea Publishing Company, New York1960. Zbl0056.06703
- CARTAN, E., Sur les domaines bornés homogènes de l'espace de variables complexes. Abh. Math. Sem. Univ. Hamburg, 11, 1935, 116-162. Zbl0011.12302
- COWEN, C. C. - POMMERENKE, CH., Inequalities for the angular derivative of an analytic function in the unit disk. J. London Math. Soc., (2), 26, 1982, 271-289. Zbl0476.30001MR675170DOI10.1112/jlms/s2-26.2.271
- DINEEN, S., The Schwarz Lemma. Oxford Mathematical Monographs, Clarendon Press, Oxford1989. Zbl0708.46046MR1033739
- EKE, B. G., On the angular derivative of regular functions. Math. Scand., 21, 1967, 122-127. Zbl0167.06301MR241617
- FAN, KY, Iteration of analytic functions of operators. Math. Z., 179, 1982, 293-298. Zbl0465.47017MR649033DOI10.1007/BF01215332
- FAN, KY, The angular derivative of an operator-valued analytic function. Pacific J. Math., 121, 1986, 67-72. Zbl0588.47018MR815033
- FRANZONI, T. - VESENTINI, E., Holomorphic Maps and Invariant Distances. North-HollandMathematics Studies40, Amsterdam-New York-Oxford1980. Zbl0447.46040MR563329
- GOLDBERG, J. L., Functions with positive real part in a half plane. Duke Math. J., 29, 1962, 333-339. Zbl0101.29702MR164041
- HARRIS, L. A., Banach algebras with involution and Möbius transformations. J. Functional Anal., 11, 1972, 1-16. Zbl0239.46058MR352994
- HARRIS, L. A., Bounded Symmetric Homogeneous Domains in Infinite Dimensional Spaces. Lecture Notes in Mathematics, 364, Springer-Verlag, Berlin-Heidelberg-New York1974, 13-40. Zbl0293.46049MR407330
- HARRIS, L. A., Operator Siegel domains. Proc. Roy. Soc. Edinburgh, 79 A, 1977, 137-156. Zbl0376.32027MR484600
- HARRIS, L. A., A generalization of -algebras. Proc. London Math. Soc., (3), 41, 1981, 331- 361. Zbl0476.46054MR607306DOI10.1112/plms/s3-42.2.331
- HARRIS, L. A., Linear fractional transformations of circular domains in operator spaces. Indiana Univ. Math. J., 41, 1992, 125-147. Zbl0760.47018MR1160906DOI10.1512/iumj.1992.41.41008
- HUA, L.-K., On the theory of automorphic functions of a matrix variable I - Geometrical Basis. Amer. J. Math., 66, 1944, 470-488. Zbl0063.02919MR11133
- HUA, L.-K., 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. Zbl0063.02920MR11134
- KAUP, W., Algebraic characterization of symmetric complex Banach manifolds. Math. Ann., 228, 1977, 39-64. Zbl0335.58005MR454091
- KAUP, W., Bounded symmetric domains in complex Hilbert spaces. Symp. Math., Istituto Nazionale di Alta Matematica Francesco Severi, 26, 1982, 11-21. Zbl0482.32012MR663020
- KIN, Y.-L., Inequalities for fixed points of holomorphic functions. Bull. London Math. Soc., 22, 1990, 446-452. Zbl0725.30012MR1082013DOI10.1112/blms/22.5.446
- KOECHER, M., An Elementary Approach to Bounded Symmetric Domain. Rice Univ., Houston, Texas1969. Zbl0217.10901MR261032
- KORANYI, A. - WOLFF, J., Generalized Cayley transformations of bounded symmetric domains. Amer. J. Math., 87, 1965, 899-939. Zbl0137.27403MR192002
- KORANYI, A. - WOLFF, J., Realization of hermitian symmetric spaces as generalized half-planes. Ann. of Math., 81, 1965, 265-288. Zbl0137.27402MR174787
- LANDAU, E. - VALIRON, G., A deduction from Schwarzs lemma. J. London Math. Soc., 4, 1929, 162-163. MR1575036JFM55.0769.02
- LOOS, O., Jordan triple systems, -spaces and bounded symmetric domains. Bull. Amer. Math. Soc., 77, 1971, 558-561. Zbl0228.32012MR281846
- LOOS, O., Bounded symmetric domains and Jordan pairs. Univ. of California, Irvine1977.
- MACCLUER, B. D. - SHAPIRO, J. H., Angular derivatives and compact composition operators on the Hardy and Bergman spaces. Canadian J. Math., 38, 1986, 878-906. Zbl0608.30050MR854144DOI10.4153/CJM-1986-043-4
- NACHBIN, L., Topology on Spaces of Holomorphic Mappings. Springer-Verlag, Berlin-Heidelberg-New York1969. Zbl0172.39902MR254579
- NEVANLINNA, R., Analytic Functions. Springer-Verlag, Berlin-Heidelberg-New York1969. Zbl0199.12501MR279280
- PJATETSKIJ-SHAPIRO, I. I., Automorphic Functions and the Geometry of Classical Domains. Gordon-Breach, New York1969. Zbl0196.09901MR252690
- POMMERENKE, CH., Univalent Functions. Vandehoeck and Ruprecht, Göttingen1975. Zbl0298.30014MR507768
- RUDIN, W., Function Theory in the Unit Ball of . Springer-Verlag, New York-Heidelberg-Berlin1980. Zbl1139.32001MR601594
- SARASON, D., Angular derivatives via Hilbert space. Complex Variables Theory Appl., 10, 1988, 1-10. Zbl0635.30024MR946094
- SHAPIRO, J. H., Composition Operators and Classical Function Theory. Springer-Verlag, New York1993. Zbl0791.30033MR1237406
- UPMEIER, H., Symmetric Banach Manifolds and Jordan -Algebras. North-Holland, Amsterdam, Math. Studies, vol. 104, 1985. Zbl0561.46032MR776786
- UPMEIER, H., Jordan algebras in analysis, operator theory, and quantum mechanics. Regional Conference Series in Math., 67, Amer. Math. Soc., Providence, RI, 1987. Zbl0608.17013MR874756
- VALIRON, G., Fonctions analytiques. Presses Univ. de France, Paris1954. Zbl0055.06702MR61658
- VESENTINI, E., Su un teorema di Wolff e Denjoy. Rend. Sem. Mat. Fis. Milano, LIII, 1983, 17-25. Zbl0596.30038MR858531DOI10.1007/BF02924880
- WARSCHAWSKI, E., Remarks on the angular derivatives. Nagoya Math. J., 42, 1971, 19-32. Zbl0209.11002MR274733
- WŁODARCZYK, K., On holomorphic maps in Banach spaces and -algebras. Quart. J. Math. Oxford, (2), 36, 1985, 495-511. Zbl0595.46048MR816489DOI10.1093/qmath/36.4.495
- WŁODARCZYK, K., Pick-Julia theorems for holomorphic maps in -algebras and Hilbert spaces. J. Math. Anal. Appl., 120, 1986, 567-571. Zbl0612.46044MR864774DOI10.1016/0022-247X(86)90179-4
- WŁODARCZYK, K., Studies of iterations of holomorphic maps in -algebras and complex Hilbert spaces. Quart. J. Math. Oxford, (2), 37, 1986, 245-256. Zbl0595.47046MR841432DOI10.1093/qmath/37.2.245
- WŁODARCZYK, K., Julia's lemma and Wolff's theorem for -algebras and complex Hilbert spaces. Proc. Amer. Math. Soc., 99, 1987, 472-476. Zbl0621.46041
- WŁODARCZYK, K., The angular derivative of Fréchet-holomorphic maps in -algebras and complex Hilbert spaces. Proc. Kon. Nederl. Akad. Wetensch., A91, 1988, 455-468; Indag. Math., 50, 1988, 455-468. Zbl0665.46034MR976528
- WŁODARCZYK, K., Hyperbolic geometry in bounded symmetric homogeneous domains of -algebras. Atti Sem. Mat. Fis. Univ. Modena, 39, 1991, 201-211. Zbl0744.46035MR1111769
- WŁODARCZYK, K., The Julia-Carathéodory theorem for distance-decreasing maps on infinite dimensional hyperbolic spaces. Rend. Mat. Acc. Lincei., s. 9, 4, 1993, 171-179. Zbl0817.46048MR1250495
- WŁODARCZYK, K., Angular limits and derivatives for holomorphic maps of infinite dimensional bounded homogeneous domains. Rend. Mat. Acc. Lincei, s. 9, 5, 1994, 43-53. Zbl0802.46060MR1273892