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arXiv · 2310.12030

Banach spaces of sequences arising from infinite matrices

Arian Bërdëllima·Naim L. Braha
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Abstract

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 J\"agers, we extend and apply some classical factorization results to the sequence spaces $\ell_M^p$.

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BibTeXRIS

Arian Bërdëllima, Naim L. Braha. 2023-10-18. Banach spaces of sequences arising from infinite matrices. https://doi.org/10.1007/s43034-024-00356-7

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