Weakly and weak$^\ast$ $p$-convergent operators
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914802466553856 |
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| author | Gabriyelyan, Saak |
| author_facet | Gabriyelyan, Saak |
| contents | Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11518 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weakly and weak$^\ast$ $p$-convergent operators Gabriyelyan, Saak Functional Analysis 46A3, 46E10 Let $p\in[1,\infty]$. Being motivated by weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between Banach spaces introduced by Fourie and Zeekoei, we introduce and study the classes of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators between arbitrary locally convex spaces. Relationships between these classes of operators are given, and we show that they have ideal properties. Numerous characterizations of weakly $p$-convergent and weak$^\ast$ $p$-convergent operators are given. |
| title | Weakly and weak$^\ast$ $p$-convergent operators |
| topic | Functional Analysis 46A3, 46E10 |
| url | https://arxiv.org/abs/2405.11518 |