Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

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