Certain topological properties for almost convergent Catalan-Motzkin sequence space

Abstract

The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the $\beta$-dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

Keywords

• Catalan numbers
• almost convergence
• sequence spaces
• core theorems

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