Absolute Lucas Spaces with Matrix and Compact Operators

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Mathematical Sciences and Applications E-Notes
Volume:10 Issue:1
Absolute Lucas Spaces with Matrix and Compact Operators

Absolute Lucas Spaces with Matrix and Compact Operators

Pages : 27-44

View : 27 | Download : 8

Publication Date : 2022-03-01

Article Type : Research Paper

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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