- Turkish Journal of Mathematics and Computer Science
- Vol: 10 Special Issue
- Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces
Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces
Authors : Hacer BİLGİN ELLİDOKUZOĞLU, Serkan DEMİRİZ
Pages : 144-152
View : 13 | Download : 3
Publication Date : 2018-12-29
Article Type : Other
Abstract :Karakaş and Karabudak [14], introduced the Lucas sequence spaces $X(E)$ and studied their some properties. The main purpose of this study is to introduce the Lucas difference sequence spaces $c_0(\hat{L},\Delta)$ and $c(\hat{L},\Delta)$ by using the Lucas sequence sequences. Also, the spaces $c_0(\hat{L},\Delta)$ and $c(\hat{L},\Delta)$, 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 $(c_0(\hat{L},\Delta) : \mu)$ and $(c(\hat{L},\Delta) : \mu)$ 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