On Some Banach Sequence Spaces Derived by a New Band Matrix

In this paper, we define the band matrixT= (tnk) bytnk=tn, k=n−1tn, k=n−10, k > n or0≤k < n−1,wheretn>0 for alln∈Nand (tn)∈c\c0. By using the matrixT, we introduce the sequencespace`p(T) for 1≤p≤ ∞. Also, we give some inclusion theorems related to this space andfind theα-,β-,γ- duals of the space`p(T). Lastly, we investigate the necessary and sufficientconditions for an infinite matrix to be in the classes (`p(T),λ) or (λ,`p(T)) and give the norm ofthe operators inB(`p(T),μ(S)), whereλ∈{`1,c0,c,`∞}andμ∈{`1,`∞}