Pełczyński's type sets and Pełczyński's geometrical properties of locally convex spaces
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910330759675904 |
|---|---|
| author | Gabriyelyan, Saak |
| author_facet | Gabriyelyan, Saak |
| contents | For $1\leq p\leq q\leq\infty$ and a locally convex space $E$, we introduce and study the $(V^\ast)$ subsets of order $(p,q)$ of $E$ and the $(V)$ subsets of order $(p,q)$ of the topological dual $E'$ of $E$. Using these sets we define and study the (sequential) Pełczyński's property $V^\ast$ of order $(p,q)$, the (sequential) Pełczyński's property $V$ of order $(p,q)$, and the Pełczyński's property $(u)$ of order $p$ in the class of all locally convex spaces. To this end, we also introduce and study several new completeness type properties, weak barrelledness conditions, Schur type properties, the Gantmacher property for locally convex spaces, and $(q,p)$-summing operators between locally convex spaces. Applications to some classical function spaces are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pełczyński's type sets and Pełczyński's geometrical properties of locally convex spaces Gabriyelyan, Saak Functional Analysis 46A03, 46A08, 46E10 For $1\leq p\leq q\leq\infty$ and a locally convex space $E$, we introduce and study the $(V^\ast)$ subsets of order $(p,q)$ of $E$ and the $(V)$ subsets of order $(p,q)$ of the topological dual $E'$ of $E$. Using these sets we define and study the (sequential) Pełczyński's property $V^\ast$ of order $(p,q)$, the (sequential) Pełczyński's property $V$ of order $(p,q)$, and the Pełczyński's property $(u)$ of order $p$ in the class of all locally convex spaces. To this end, we also introduce and study several new completeness type properties, weak barrelledness conditions, Schur type properties, the Gantmacher property for locally convex spaces, and $(q,p)$-summing operators between locally convex spaces. Applications to some classical function spaces are given. |
| title | Pełczyński's type sets and Pełczyński's geometrical properties of locally convex spaces |
| topic | Functional Analysis 46A03, 46A08, 46E10 |
| url | https://arxiv.org/abs/2402.08860 |