Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Factorization of holomorphic mappings
on $C(K)$-spaces

Author: Jari Taskinen
Journal: Proc. Amer. Math. Soc. 125 (1997), 2337-2346
MSC (1991): Primary 46G20; Secondary 47H99
MathSciNet review: 1377010
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a universal mapping theorem for a large class of holomorphic mappings $F$ on a $C(K)$-space, stating that $F$ can be locally written in the form $F(f) = B \bigl ( 1 /( 1 - Af) \bigr ), $ where $A$ and $B $ are bounded linear operators on certain Banach spaces consisting of functions on $K$, and the division is taken pointwise.

References [Enhancements On Off] (What's this?)

  • [A] R. Aron, Holomorphy types for open subsets of a Banach space, Studia Math. 45 (1973), 273-289. MR 49:5838
  • [C] S. B. Chae, Calculus and holomorphy in normed spaces, Marcel Dekker, New York, 1985.
  • [D1] S. Dineen, Holomorphy types on Banach spaces, Studia Math. 39 (1971), 241-288. MR 46:3837
  • [D2] S. Dineen, Complex analysis in locally convex spaces, North Holland Mathematics Studies, vol. 57, 1981. MR 84b:46050
  • [G-G--M] P. Galindo, D. Garcia, M. Maestre, Holomorphic mappings of bounded type, J. Math. Anal. Appl. 166.1. (1992), 236-246. MR 94b:46069
  • [H] B. Hoffmann, An injective characterization of Peano spaces, Topol. and Appl. 11 (1980), 37-46. MR 80m:54049
  • [Ku] K. Kuratowski, Topology, vol. I, Academic Press, New York and London, 1966. MR 36:840
  • [LT] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces, Springer Lecture Notes in Mathematics 338 (1973). MR 54:3344
  • [LT1] J. Lindenstrauss, L. Tzafriri, Classical Banach Spaces I., Springer, Berlin-Heidelberg-New York, 1977.
  • [Ma] P. Mazet, Analytic sets in locally convex spaces, North-Holland Mathematics Studies, vol. 120, North-Holland, Amsterdam, 1986.
  • [Mu1] J. Mujica, Linearization of bounded holomorphic mappings on Banach spaces, Trans. Amer. Math. Soc. 324 (1991), 867-887. MR 91h:46088
  • [Mu2] J. Mujica, Linearization of holomorphic mappings of bounded type, Progress in Functional Analysis (K. D. Bierstedt, J. Bonet, J. Horvath, M. Maestre, eds.), vol. 170, North-Holland Mathematics Studies, 1992, pp. 149-162. MR 93k:46037
  • [Mu-N] J. Mujica , L. Nachbin, Linearization of holomorphic mappings on locally convex spaces, J. Math. Pures Appl. 71 (1992), 543-560. MR 93k:46038
  • [P] A. Pe{\l}czy\'{n}ski, Linear extensions, linear averaging and application to linear topological classification of spaces of continuous functions, Rozprawy Matematyczne 58 (1968). MR 37:3335
  • [R] R. A. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, Ph.D thesis, Trinity College, Dublin, 1980.
  • [T1] J. Taskinen, An application of averaging operators to multilinearity, Math. Ann. 297 (1993), 567-572. MR 94j:46031
  • [T2] J. Taskinen, Linearization of holomorphic mappings on $C(K)$-spaces, Isr. J. Math. 92 (1995), 1-3, 207-219. MR 96h:46065
  • [T3] J. Taskinen, A continuous surjection from the unit interval onto the unit square, Rev.Mat.Univ. Complutense Madrid 6.1 (1993), 101-120. MR 94i:46023
  • [T4] -, An infinite polynomially non-linear system of equations, J. Math. Anal. Appl. 200 (1996), 591-613. CMP 96:13

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46G20, 47H99

Retrieve articles in all journals with MSC (1991): 46G20, 47H99

Additional Information

Jari Taskinen
Affiliation: Department of Mathematics, P.O. Box 4 (Hallituskatu 15), Fin-00014 University of Helsinki, Finland
Email: Jari.Taskinen@Helsinki.Fi

Received by editor(s): August 16, 1995
Received by editor(s) in revised form: February 20, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society