Motzkin Sequence Spaces and Motzkin Core

Abstract

In the current work, it is constructed the Motzkin matrix obtained by using Motzkin numbers $\mathcal{M}=({\mathfrak{m}}_{\mathit{\text{rs}}})$ and is examined the sequence spaces $c(\mathcal{M})$ and $c_0(\mathcal{M})$ described as the domain of Motzkin matrix $\mathcal{M}$ 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 $c(\mathcal{M})$ and $c_0(\mathcal{M})$ 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.

Keywords:

• Core theorems
• Köthe duals
• matrix transformations
• Motzkin numbers
• sequence spaces

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 11B83
• 46A45
• 40A05
• 46A35