Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

Authors : Hacer BİLGİN ELLİDOKUZOĞLU, Serkan DEMİRİZ

Pages : 144-152

View : 57 | Download : 15

Publication Date : 2018-12-29

Article Type : Conference Paper

Abstract :Karakaş and Karabudak [14], introduced the Lucas  sequence spaces $Xinsert ignore into journalissuearticles values(E);$  and studied  their some properties. The main purpose of this study is to  introduce the Lucas difference sequence spaces $c_0insert ignore into journalissuearticles values(\hat{L},\Delta);$ and $cinsert ignore into journalissuearticles values(\hat{L},\Delta);$  by using the Lucas sequence sequences. Also, the spaces $c_0insert ignore into journalissuearticles values(\hat{L},\Delta);$ and $cinsert ignore into journalissuearticles values(\hat{L},\Delta);$, are linearly  isomorphic to spaces $c_0$ and $c$, respectively, have been proved. Besides this, the $\alpha-,\beta-$ and  $\gamma-$duals of this spaces have been computed, their  bases have been constructed and some topological properties of these  spaces have been studied. Finally, the classes of matrices  $insert ignore into journalissuearticles values(c_0insert ignore into journalissuearticles values(\hat{L},\Delta); : \mu);$ and $insert ignore into journalissuearticles values(cinsert ignore into journalissuearticles values(\hat{L},\Delta); : \mu);$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty, c$ and $c_0$ and derives the other  characterizations for the special cases of $\mu$.
Keywords : Lucas sequence spaces, matrix domain

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