On The Difference Sequence Space $l_p(hat{T}^q)$

Authors : Merve İLKHAN, Pınar ZENGİN ALP

Pages : 161-173

Doi:10.36753/mathenot.597703

View : 36 | Download : 7

Publication Date : 2019-10-15

Article Type : Research Paper

Abstract :In this study, we introduce a new matrix $\hat{T}^q=insert ignore into journalissuearticles values(\hat{t}^q_{nk});$ by \[ \hat{t}^q_{nk}=\left \{ \begin{array} [c]{ccl}% \frac{q_n}{Q_n} t_n & , & k=n\\ \frac{q_k}{Q_n}t_k-\frac{q_{k+1}}{Q_n} \frac{1}{t_{k+1}} & , & kn . \end{array} \right. \] where $t_k>0$ for all $n\in\mathbb{N}$ and $insert ignore into journalissuearticles values(t_n);\in c\backslash c_0$ . By using the matrix $\hat{T}^q$ , we introduce the sequence space $\ell_pinsert ignore into journalissuearticles values(\hat{T}^q);$ for $1\leq p\leq\infty$ . In addition, we give some theorems on inclusion relations associated with $\ell_pinsert ignore into journalissuearticles values(\hat{T}^q);$ and find the $\alpha$ -, $\beta$ -, $\gamma$ - duals of this space. Lastly, we analyze the necessary and sufficient conditions for an infinite matrix to be in the classes $insert ignore into journalissuearticles values(\ell_pinsert ignore into journalissuearticles values(\hat{T}^q);,\lambda);$ or $insert ignore into journalissuearticles values(\lambda,\ell_pinsert ignore into journalissuearticles values(\hat{T}^q););$ , where $\lambda\in\{\ell_1,c_0,c,\ell_\infty\}$ .
Keywords : sequence spaces, matrix transformations, Schauder basis, alpha eta gamma duals

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