On Some Properties of Banach Space-Valued Fibonacci Sequence Spaces

Authors : Yılmaz Yılmaz, Seçkin Yalçın

Pages : 80-87

Doi:10.33434/cams.1442975

View : 53 | Download : 63

Publication Date : 2024-06-30

Article Type : Research Paper

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