Factorization of uniformly holomorphic functions

Volume 61 / 1995

Luiza Moraes, Otilia Paques, M. Zaine Annales Polonici Mathematici 61 (1995), 1-11 DOI: 10.4064/ap-61-1-1-11


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.


  • Luiza Moraes
  • Otilia Paques
  • M. Zaine

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