Some Algebraic and Topological Properties of New Lucas Difference Sequence Spaces

Abstract

Karakas¸ and Karabudak [22], 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 c0(Lˆ, ?) and c(Lˆ, ?) by using the Lucas sequence. Also, we prove that the spaces c0(Lˆ, ?) and c(Lˆ, ?), are linearly isomorphic to spaces c0 and c, respectively. Besides this, the ??, ?? and ??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 (c0(Lˆ, ?) : µ) and (c(Lˆ, ?) : µ) have been characterized, where µ is one of the sequence spaces `?, c and c0 and derives the other characterizations for the special cases of µ.