On some Geometric Properties of Some Catalan Sequence Spaces

Year 2025, Volume: 17 Issue: 2, 485 - 495, 30.12.2025

Yılmaz Yılmaz , Seçkin Yalçın , Halise Levent , Hacer Bozkurt

https://doi.org/10.47000/tjmcs.1690548

Abstract

It is important to know whether a Banach space is rotund or smooth when
examining the structural properties of the space, especially its geometric
properties. Gateaux differentiability of the norm of the space has an
important place in the discussion of smoothness. In this study, we examined
such properties of the sequence spaces $\ell _{p}(\widetilde{C}),$ $1\leq
p<\infty ,$ and $\ell _{\infty }(\widetilde{C})$ constructed by the sequence of Catalan numbers. We have also shown that some types of these spaces have elite structural properties such as Approximation and Dunford-Pettis Properties.

Keywords

Catalan numbers , approximation property , Dunford-Pettis property , smoothness , rotundity

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