# Factorization of uniformly holomorphic functions

Luiza A. Moraes; Otilia W. Paques; M. Carmelina F. Zaine

Annales Polonici Mathematici (1995)

- Volume: 61, Issue: 1, page 1-11
- ISSN: 0066-2216

## Access Full Article

top## Abstract

top## How to cite

topLuiza A. Moraes, Otilia W. Paques, and M. Carmelina F. Zaine. "Factorization of uniformly holomorphic functions." Annales Polonici Mathematici 61.1 (1995): 1-11. <http://eudml.org/doc/262358>.

@article{LuizaA1995,

abstract = {Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the pull-back $ε*_\{u\}(U)$ of the envelope of uniform holomorphy of Π(U) constructed by Paques and Zaine [9] is the envelope of uF-holomorphy of U.},

author = {Luiza A. Moraes, Otilia W. Paques, M. Carmelina F. Zaine},

journal = {Annales Polonici Mathematici},

keywords = {uniformly holomorphic; envelope of holomorphy; canonical quotient mapping; factorization of uniformly holomorphic functions; envelope of -holomorphy; pull-back},

language = {eng},

number = {1},

pages = {1-11},

title = {Factorization of uniformly holomorphic functions},

url = {http://eudml.org/doc/262358},

volume = {61},

year = {1995},

}

TY - JOUR

AU - Luiza A. Moraes

AU - Otilia W. Paques

AU - M. Carmelina F. Zaine

TI - Factorization of uniformly holomorphic functions

JO - Annales Polonici Mathematici

PY - 1995

VL - 61

IS - 1

SP - 1

EP - 11

AB - Let E be a complex Hausdorff locally convex space such that the strong dual E’ of E is sequentially complete, let F be a closed linear subspace of E and let U be a uniformly open subset of E. We denote by Π: E → E/F the canonical quotient mapping. In §1 we study the factorization of uniformly holomorphic functions through π. In §2 we study F-quotients of uniform type and introduce the concept of envelope of uF-holomorphy of a connected uniformly open subset U of E. The main result states that the pull-back $ε*_{u}(U)$ of the envelope of uniform holomorphy of Π(U) constructed by Paques and Zaine [9] is the envelope of uF-holomorphy of U.

LA - eng

KW - uniformly holomorphic; envelope of holomorphy; canonical quotient mapping; factorization of uniformly holomorphic functions; envelope of -holomorphy; pull-back

UR - http://eudml.org/doc/262358

ER -

## References

top- [1] R. Aron, L. Moraes and R. Ryan, Factorization of holomorphic mappings in infinite dimensions, Math. Ann. 277 (1987), 617-628. Zbl0611.46053
- [2] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, Amsterdam, 1981. Zbl0484.46044
- [3] P. Hilton, Tópicos de Álgebra Homológica, 8º Colóquio Brasileiro de Matemática, IME-Universidade de S ao Paulo, Brasil, 1971.
- [4] L. Moraes, O. W. Paques and M. C. F. Zaine, F-quotients and envelope of F-holomorphy, J. Math. Anal. Appl. 163 (2) (1992), 393-405. Zbl0789.46041
- [5] J. Mujica, Domain of holomorphy in (DFC)-spaces, in: Functional Analysis, Holomorphy and Approximation Theory, Lecture Notes in Math. 843, Springer, Berlin, 1980, 500-533.
- [6] L. Nachbin, Uniformité d'holomorphie et type exponentiel, in: Séminaire P. Lelong 1970, Lectures Notes in Math. 205, Springer, Berlin, 1971, 216-224. Zbl0218.46024
- [7] L. Nachbin, Recent developments in infinite dimensional holomorphy, Bull. Amer. Math. Soc. 79 (1973), 625-640. Zbl0279.32017
- [8] L. Nachbin, On pure uniform holomorphy in spaces of holomorphic germs, Results in Math. 8 (1985), 117-122. Zbl0613.46030
- [9] O. W. Paques and M. C. Zaine, Uniformly holomorphic continuation, J. Math. Anal. Appl. 123 (2) (1987), 448-454. Zbl0631.46043
- [10] M. Schottenloher, The Levi problem for domains spread over locally convex spaces with a finite dimensional Schauder decomposition, Ann. Inst. Fourier (Grenoble) 26 (4) (1976), 207-237. Zbl0309.32013

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.