@article {
author = {Roopaei, Hadi and Foroutannia, Davoud},
title = {A new sequence space and norm of certain matrix operators on this space},
journal = {Sahand Communications in Mathematical Analysis},
volume = {03},
number = {1},
pages = {1-12},
year = {2016},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {},
abstract = {In the present paper, we introduce the sequence space \[{l_p}(E,\Delta) = \left\{ x = (x_n)_{n = 1}^\infty : \sum_{n = 1}^\infty \left| \sum_{j \in {E_n}} x_j - \sum_{j \in E_{n + 1}} x_j\right| ^p < \infty \right\},\] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $p\ge 1$. We investigate its topological properties and inclusion relations. Moreover, we consider the problem of finding the norm of certain matrix operators from $l_p$ into $ l_p(E,\Delta)$, and apply our results to Copson and Hilbert matrices.},
keywords = {Difference sequence space,Matrix domains,norm,Copson matrix,Hilbert matrix},
url = {https://scma.maragheh.ac.ir/article_18569.html},
eprint = {https://scma.maragheh.ac.ir/article_18569_d37578addf12775560a0dd1348a14dea.pdf}
}