A class of weighted composition operators whose Range and Null spaces are complemented
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909106093162496 |
|---|---|
| author | Patel, Anurag Kumar |
| author_facet | Patel, Anurag Kumar |
| contents | In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$ whose range space is of finite co-dimension. Thereafter, we characterize a class of weighted composition operators whose range space is a complemented subspace. Lastly, we characterize weighted composition operators on $\ell_p$ which are Fredholm operators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08972 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A class of weighted composition operators whose Range and Null spaces are complemented Patel, Anurag Kumar Functional Analysis 46B25, 54B15, 47B33, 47A53 In this paper, we prove that the null space of a weighted composition operator on $\ell_p~ (1 \leq p < \infty)$ is a complemented subspace. We also give a necessary and sufficient condition for a weighted composition operator on $\ell_p$ whose range space is of finite co-dimension. Thereafter, we characterize a class of weighted composition operators whose range space is a complemented subspace. Lastly, we characterize weighted composition operators on $\ell_p$ which are Fredholm operators. |
| title | A class of weighted composition operators whose Range and Null spaces are complemented |
| topic | Functional Analysis 46B25, 54B15, 47B33, 47A53 |
| url | https://arxiv.org/abs/2402.08972 |