Absolute Lucas Spaces with Matrix and Compact Operators

Year 2022, Volume: 10 Issue: 1, 27 - 44, 01.03.2022

Fadime Gökçe

https://doi.org/10.36753/mathenot.816576

Cited By: 1

Abstract

The main purpose of this study is to introduce the absolute Lucas series spaces and to investigate their some algebraic and topological structure such as some inclusion relations, $BK-$ to this space, duals and Schauder basis. Also, the characterizations of matrix operators related to these space with their norms are given. Finally, by using Hausdorff measure of noncompactness, the necessary and sufficient conditions for a matrix operator on them to be compact are obtained.

Keywords

Absolute summability, Lucas numbers, matrix transformations, sequence spaces, Hausdroff measures of noncompactness, Operator norm, bounded operators

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