Almost convergent Motzkin sequence spaces and core theorems

Abstract

In this article, we present and investigate new type of sequence spaces called by almost convergent Motzkin sequence spaces. We demonstrate that this newly introduced space is linearly isomorphic to the space of all almost convergent sequences and compute the $\beta-$dual. Additionally, we characterize $(\mathfrak M, Z)$ and $(Z,\mathfrak M)$ for any given sequence space $Z$, and also determine the necessary and sufficient condition on a matrix $\mathcal P$  such that for every bounded sequence $u$, $B_{\mathcal M}$-core$(\mathcal P u)\subseteq K$-core$(u)$ and $B_{\mathcal M}$-core$(\mathcal P u)\subseteq st$-core$(u)$.