Extension of $p$-compact operators in Banach spaces
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917222674333696 |
|---|---|
| author | Karak, Sainik Paul, Tanmoy |
| author_facet | Karak, Sainik Paul, Tanmoy |
| contents | We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these extension properties when the underlying spaces, either domain or codomain, are $P_λ$ spaces. We also answer if these extensions are almost norm-preserving in such circumstances where the extension $\widetilde{T}$ of a $T$ exists. It is observed that an operator can often be extended to a larger domain when the codomain is appropriately extended as well. Specific assumptions might enable us to obtain an extension of an operator that maintains the same range. Necessary and sufficient conditions are derived for a Banach space to be $L_1$-predual. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_01021 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extension of $p$-compact operators in Banach spaces Karak, Sainik Paul, Tanmoy Functional Analysis 46B20, 46B28, 46B50, 47B07, 46B10, 46B25 We analyze various consequences in relation to the extension of operators $T:X\to Y$ that are $p$-compact, as well as the extension of operators $T:X\to Y$ whose adjoints $T^*:Y^*\to X^*$ are $p$-compact. In most cases, we discuss these extension properties when the underlying spaces, either domain or codomain, are $P_λ$ spaces. We also answer if these extensions are almost norm-preserving in such circumstances where the extension $\widetilde{T}$ of a $T$ exists. It is observed that an operator can often be extended to a larger domain when the codomain is appropriately extended as well. Specific assumptions might enable us to obtain an extension of an operator that maintains the same range. Necessary and sufficient conditions are derived for a Banach space to be $L_1$-predual. |
| title | Extension of $p$-compact operators in Banach spaces |
| topic | Functional Analysis 46B20, 46B28, 46B50, 47B07, 46B10, 46B25 |
| url | https://arxiv.org/abs/2511.01021 |