On Some Banach Sequence Spaces Derived by a New Band Matrix
Emrah Evren Kara
Duzce University, Department of Mathematics, Düzce, Turkey.
Merve İlkhan *
Duzce University, Department of Mathematics, Düzce, Turkey.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we de_ne the band matrix T = (tnk) by
where tn > 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 ∝-, B-, γ- duals of the space `p(T). Lastly, we investigate the necessary and su_cient conditions for an in_nite 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; `1}.
Keywords: Sequence spaces, matrix transformations, Schauder basis, α-; β-; γ-duals.