Banach spaces of sequences arising from infinite matrices

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 \(\Vert \cdot \Vert _{M,p}\), we prove some basic properties of the Banach spaces of sequences \((\ell _M^p,\Vert \cdot \Vert _{M,p})\). 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 \(\ell _M^p\).