On the block sequence space $l_p(E)$ and related matrix transformations

Authors: DAVOUD FOROUTANNIA

Abstract: The purpose of the present study is to introduce the sequence space $$l_p(E)=\left\{ x=(x_n)_{n=1}^{\infty}\;:\; \sum_{n=1}^{\infty} \left|\sum_{j\in E_n}x_j\right|^p<\infty\right\},$$ where $E=(E_n)$ is a partition of finite subsets of the positive integers and $1\le p<\infty$. We investigate some topological properties of this space and also give some inclusion relations concerning it. Furthermore, we compute $\alpha$- and $\beta$-duals of this space and characterize the matrix transformations from the space $l_p(E)$ to the space $X$, where $X\in\{l_{\infty}, c, c_0\}$.

Keywords: Sequence spaces, matrix domains, $\alpha$- and $\beta$-duals, matrix transformations

Full Text: PDF