Dineen, Seán; Moraes, Luiza A. Holomorphic functions on strict inductive limits of Banach spaces. (English) Zbl 0789.46039 Rev. Mat. Univ. Complutense Madr. 5, No. 2-3, 177-183 (1992). Summary: 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. Cited in 1 Document MSC: 46G20 Infinite-dimensional holomorphy 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) Keywords:set of holomorphic functions on a strict inductive limit PDFBibTeX XMLCite \textit{S. Dineen} and \textit{L. A. Moraes}, Rev. Mat. Univ. Complutense Madr. 5, No. 2--3, 177--183 (1992; Zbl 0789.46039) Full Text: EuDML