On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces

Year 2024, Volume: 7 Issue: 2, 80 - 87, 30.06.2024

Yılmaz Yılmaz , Seçkin Yalçın

https://doi.org/10.33434/cams.1442975

Abstract

In this work, we give some results about the basic properties of the vector-valued Fibonacci sequence spaces. In general, sequence spaces with Banach space-valued cannot have a Schauder Basis unless the terms of the sequences are complex or real terms. Instead, we defined the concept of relative basis in \cite{yy2} by generalizing the definition of a basis in Banach spaces. Using this definition, we have characterized certain important properties of vector-term Fibonacci sequence spaces, such as separability, Dunford-Pettis Property, approximation property, Radon-Riesz Property and Hahn-Banach extension property.

Keywords

Approximation property, Dunford-Pettis property, Fibonacci sequence spaces, Radon-Riesz property, Vector-Valued sequence spaces

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