Full paper in PDF:
$%S. Dineen and L. A. Moraes, Holomorphic functions on strict inductive limits of
Banach spaces, Rev. Mat. Univ. Complut. Madrid 5 (1992), no. 2, 3, 177-183.%$
Holomorphic Functions on Strict Inductive Limits of Banach Spaces
Department of Mathematics University College Dublin Belfield, Dublin 4 — Ireland | Instituto de Matemática Universidade Federal do Rio de Janeiro Caixa Postal 68530 21945 Rio de janeiro — Brazil |
In this article we show that a number of apparently different properties coincide on the set of holomorphic functions on a strict inductive limit (all inductive limits are assumed to be countable and proper) of Banach spaces and that they are all satisfied only in the trivial case of a strict inductive limit of finite dimensional spaces. Thus the linear properties of a strict inductive limit of Banach spaces rarely translate themselves into holomorphic properties.
1991 Mathematics Subject Classification: 46G20.