On Some Banach Sequence Spaces Derived by a New Band Matrix

Abstract

In this paper, we define the band matrix T = (tnk) by tnk =  tn , k = n − 1 tn , k = n− 1 0 , k > n or 0 ≤ k 0 for all n ∈ N and (tn) ∈ c\c0. By using the matrix T , we introduce the sequence space `p(T ) for 1 ≤ p ≤ ∞. Also, we give some inclusion theorems related to this space and find the α-, β-, γduals of the space `p(T ). Lastly, we investigate the necessary and sufficient conditions for an infinite matrix to be in the classes (`p(T ), λ) or (λ, `p(T )) and give the norm of the operators in B(`p(T ), μ(S)), where λ ∈ {`1, c0, c, `∞} and μ ∈ {`1, `∞}.