The Denjoy-Wolff Theorem in the Open Unit Ball of a Strictly Convex Banach Space

Advances in Mathematics

Volumn 143, Issue 1, 1999, Pages 111-123

  Kapeluszny, Jaroslaw ^a   Kuczumow, Tadeusz ^a   Reich, Simeon ^b  

^a MARIA CURIE SK ODOWSKA UNIVERSITY   (Poland)

^b TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

Horospheres; Iterates of a holomorphic mapping; The Denjoy Wolff theorem; The Kobayashi distance

Indexed keywords

EID: 0039819759     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.1998.1786     Document Type: Article

References (34)

1. Abate M. Horospheres and iterates of holomorphic maps. Math. Z. 198:1988;225-238.
2. Abate M. Iteration theory, compactly divergent sequences and commuting holomorphic maps. Ann. Scuola Norm. Sup. Pisa. 18:1991;167-191.
3. Abate M. Iteration Theory of Holomorphic Maps on Taut Manifolds. 1989;Mediterranean Press.
4. Burckel R. B. Iterating analytic self-maps of discs. Am. Math. Mon. 88:1981;396-407.
5. Calka A. On conditions under which isometries have bounded orbits. Colloq. Math. 48:1984;219-227.
6. Chae S. B. Holomorphy and Calculus in Normed Spaces. 1985;Dekker, New York.
7. Chu C.-H., Mellon P. Iteration of compact holomorphic maps on a Hilbert ball. Proc. Amer. Math. Soc. 125:1997;1771-1777.
8. Denjoy A. Sur l'iteration des fonctions analytiques. C.R. Acad. Sc. Paris. 182:1926;255-257.
9. Dineen S., Timoney R. M., Vigué J.-P. Pseudodistances invariantes sur les domaines d'un espace localement convexe. Ann. Scuola Norm. Sup. Pisa. 12:1985;515-529.
10. Earle C. J., Hamilton R. S. A fixed point theorem for holomorphic mappings. Proc. Symp. Pure Math. 1970;Amer. Math. Soc. Providence. p. 61-65.
11. Edelstein M. The construction of an asymptotic center with a fixed point property. Bull. Amer. Math. Soc. 78:1972;206-208.
12. Franzoni T., Vesentini E. Holomorphic Maps and Invariant Distances. 1980;North-Holland, Amsterdam.
13. Goebel K. Fixed points and invariant domains of holomorphic mappings of the Hilbert ball. Nonlinear Anal. 6:1982;1327-1334.
14. Goebel K., Kirk W. A. Topics in Metric Fixed Point Theory. 1990;Cambridge Univ. Press, Cambridge.
15. Goebel K., Reich S. Iterating holomorphic self-mappings of the Hilbert ball. Proc. Japan Acad. 58:1982;349-352.
16. Goebel K., Reich S. Uniform Convexity, Hyperbolic Geometry and Nonexpansive Mappings. 1984;Dekker, New York.
17. Goebel K., Sekowski T., Stachura A. Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball. Nonlinear Anal. 4:1980;1011-1021.
18. Harris L. A. Schwarz-Pick systems of pseudometrics for domains in normed linear spaces. Advances in Holomorphy. 1979;North Holland, Amsterdam. p. 345-406.
19. Hervé M. Quelques propriétés des applications analytiques d'une boule à m dimensions dans elle-même. J. Math. Pures et Appl. 42:1963;117-147.
20. BH. Ann. Univ. Mariae Curie-Sklodowska Sect. A. 51:1997;179-183.
21. Kubota Y. Iteration of holomorphic maps of the unit ball into itself. Proc. Amer. Math. Soc. 88:1983;476-480.
22. n. Adv. Math. 81:1990;90-98.
23. Lempert L. Holomorphic retracts and intrinsic metrics in convex domains. Anal. Math. 8:1982;257-261.
24. n. Michigan Math. J. 30:1983;97-106.
25. Reich S. Averaged mappings in the Hilbert ball. J. Math. Anal. Appl. 109:1985;199-206.
26. n. 1980;Springer-Verlag, Berlin.
27. Schauder J. Der Fixpunktsatz in Funktionalräumen. Studia Math. 2:1930;171-180.
28. Stachura A. Iterates of holomorphic self-maps of the unit ball in Hilbert spaces. Proc. Amer. Math. Soc. 93:1985;88-90.
29. Thorp E., Whitley R. The strong maximum modulus theorem for analytic functions into a Banach space. Proc. Amer. Math. Soc. 18:1967;640-646.
30. Vesentini E. Invariant distances and invariant differential metrics in locally convex spaces. Spectral Theory. 8:1982;493-512.
31. Vesentini E. Su un teorema di Wolff e Denjoy. Rend. Sem. Mat. Fis. Milano. 53:1983;17-25.
32. Vesentini E. Iteration of holomorphic maps. Russ. Math. Surveys. 40:1985;7-11.
33. Wolff J. Sur l'iteration des fonctions bornees. C.R. Acad. Sc. Paris. 182:1926;42-43.
34. P. Yang, Holomorphic curves and boundary regularity of biholomorphic maps of pseudoconvex domains, 1978.