Abstract
In the current work, it is constructed the Motzkin matrix obtained by using Motzkin numbers M = ( m rs ) and is examined the sequence spaces c ( M ) and c 0 ( M ) described as the domain of Motzkin matrix M in the spaces c and c 0, 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 c 0 ( 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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