Almost convergent Motzkin sequence spaces and core theorems

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