Abstract
Matrix F̂ derived from the Fibonacci sequence was first introduced by Kara (2013) and the spaces lp(F) and l∞(F); (1 ≤ p < ∞) were examined. Then, Başarır et al. (2015) defined the spaces c0(F) and c(F) and Candan (2015) examined the spaces c(F(r,s)) and c0(F(r,s)). Later, Yaşar and Kayaduman (2018) defined and studied the spaces cs(F(s,r)) and bs(F(s,r)). In this study, we built the spaces cs(F) and bs(F). They are the domain of the matrix F on cs and bs, where F is a triangular matrix defined by Fibonacci Numbers. Some topological and algebraic properties, isomorphism, inclusion relations and norms, which are defined over them are examined. It is proven that cs(F) and bs(F) are Banach spaces. It is determined that they have the γ, β, α -duals. In addition, the Schauder base of the space cs(F) are calculated. Finally, a number of matrix transformations of these spaces are found.
Highlights
Cooke [1] formulated the theory of infinite matrices in the book “Infinite Matrices and SequenceSpaces”
We address the question: What are the properties of the domain of the Fibonacci band matrix on sequence spaces bs and cs? The domain of the Fibonacci band matrix creates a new sequence space
One difficulty of this study is to determine whether the new space is the contraction or the expansion, or the overlap of the original space
Summary
Cooke [1] formulated the theory of infinite matrices in the book “Infinite Matrices and SequenceSpaces”.
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