Spaceability of special families of null sequences of holomorphic functions
Abstract
Abstract In this note, we consider the space $$H(\Omega )^{\mathbb {N}}$$ H ( Ω ) N of sequences of holomorphic functions on an open set $$\Omega \subset \mathbb {C}$$ Ω ⊂ C . If $$H(\Omega )$$ H ( Ω ) is endowed with its natural topology and $$H(\Omega )^{\mathbb {N}}$$ H ( Ω ) N is endowed with the product topology, then it is proved the existence of two closed infinite-dimensional vector subspaces of $$H(\Omega )^{\mathbb {N}}$$ H ( Ω ) N such that all nonzero members of the first subspace are sequences tending to zero pointwise but not compactly on $$\Omega $$ Ω and all nonzero members of the second subspace are sequences tending to zero compactly but not uniformly on $$\Omega $$ Ω . This complements the results provided in a recent work by the same authors.
Fields of Study & Subjects
Advanced Banach Space Theory
Holomorphic and Operator Theory
Analytic and geometric function theory
Publication details
- Journal / source
- Banach Journal of Mathematical Analysis
- Publisher
- Springer Science and Business Media LLC
- Volume
- 20
- Issue
- 2
- Publication date
- 10 March 2026
- Language
- EN