Banach spaces of sequences arising from infinite matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909532010053632 |
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| author | Bërdëllima, Arian Braha, Naim L. |
| author_facet | Bërdëllima, Arian Braha, Naim L. |
| contents | Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences $(\ell_M^p,\|\cdot\|_{M,p})$. In particular we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices $M$ for all $p>1$. A special attention is given to the identification of the dual space $(\ell_M^p )^*$. Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces $\ell_M^p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_12030 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Banach spaces of sequences arising from infinite matrices Bërdëllima, Arian Braha, Naim L. Functional Analysis 46B45, 46B10, 46B20, 46B04, 46B03 Given an infinite matrix $M=(m_{nk})$ we study a family of sequence spaces $\ell_M^p$ associated with it. When equipped with a suitable norm $\|\cdot\|_{M,p}$ we prove some basic properties of the Banach spaces of sequences $(\ell_M^p,\|\cdot\|_{M,p})$. In particular we show that such spaces are separable and strictly/uniformly convex for a considerably large class of infinite matrices $M$ for all $p>1$. A special attention is given to the identification of the dual space $(\ell_M^p )^*$. Building on the earlier works of Bennett and Jägers, we extend and apply some classical factorization results to the sequence spaces $\ell_M^p$. |
| title | Banach spaces of sequences arising from infinite matrices |
| topic | Functional Analysis 46B45, 46B10, 46B20, 46B04, 46B03 |
| url | https://arxiv.org/abs/2310.12030 |