Spaceability of special families of null sequences of holomorphic functions
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908876772737024 |
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| author | Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. |
| author_facet | Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. |
| contents | In this note, we consider the space $H(Ω)^{\mathbb N}$ of sequences of holomorphic functions on an open set $Ω\subset {\mathbb C}$. If $H(Ω)$ is endowed with its natural topology and $H(Ω)^{\mathbb N}$ is endowed with the product topology, then it is proved the existence of two closed infinite dimensional vector subspaces of $H(Ω)^{\mathbb N}$ such that all nonzero members of the first subspace are sequences tending to zero pointwisely but not compactly on $Ω$ and all nonzero members of the second subspace are sequences tending to zero compactly but not uniformly on $Ω$. This complements the results provided in a recent work by the same authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07048 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spaceability of special families of null sequences of holomorphic functions Bernal-González, L. Calderón-Moreno, M. C. López-Salazar, J. Prado-Bassas, J. A. Complex Variables Functional Analysis 15A03, 30H50, 40A30, 46E10, 46B87 In this note, we consider the space $H(Ω)^{\mathbb N}$ of sequences of holomorphic functions on an open set $Ω\subset {\mathbb C}$. If $H(Ω)$ is endowed with its natural topology and $H(Ω)^{\mathbb N}$ is endowed with the product topology, then it is proved the existence of two closed infinite dimensional vector subspaces of $H(Ω)^{\mathbb N}$ such that all nonzero members of the first subspace are sequences tending to zero pointwisely but not compactly on $Ω$ and all nonzero members of the second subspace are sequences tending to zero compactly but not uniformly on $Ω$. This complements the results provided in a recent work by the same authors. |
| title | Spaceability of special families of null sequences of holomorphic functions |
| topic | Complex Variables Functional Analysis 15A03, 30H50, 40A30, 46E10, 46B87 |
| url | https://arxiv.org/abs/2505.07048 |