In the current work, it is constructed the Motzkin matrix obtained by using Motzkin numbers M=(mrs) and is examined the sequence spaces c(M) and c0(M) described as the domain of Motzkin matrix M in the spaces c and c0, respectively. It is investigated topological properties, established Schauder basis and stated Köthe duals of the aforementioned spaces. Additionally, it is characterized the matrix classes from c(M) and c0(M) to the classical sequence spaces and vice versa. Finally, Motzkin core of any sequence is presented and it is elaborated some inclusion relation of just described new type of core.
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Erdem et al. (2024) studied this question.