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

Abstract

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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.

How to cite

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Luiza 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

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  1. [1] R. Aron, L. Moraes and R. Ryan, Factorization of holomorphic mappings in infinite dimensions, Math. Ann. 277 (1987), 617-628. Zbl0611.46053
  2. [2] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, Amsterdam, 1981. Zbl0484.46044
  3. [3] P. Hilton, Tópicos de Álgebra Homológica, 8º Colóquio Brasileiro de Matemática, IME-Universidade de S ao Paulo, Brasil, 1971. 
  4. [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. [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. [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. [7] L. Nachbin, Recent developments in infinite dimensional holomorphy, Bull. Amer. Math. Soc. 79 (1973), 625-640. Zbl0279.32017
  8. [8] L. Nachbin, On pure uniform holomorphy in spaces of holomorphic germs, Results in Math. 8 (1985), 117-122. Zbl0613.46030
  9. [9] O. W. Paques and M. C. Zaine, Uniformly holomorphic continuation, J. Math. Anal. Appl. 123 (2) (1987), 448-454. Zbl0631.46043
  10. [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

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