University of MaraghehSahand Communications in Mathematical Analysis2322-580703120160201A new sequence space and norm of certain matrix operators on this space11218569ENHadiRoopaeiDepartment of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.DavoudForoutanniaDepartment of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran.Journal Article20151006In 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_jright| ^p < infty right},] where $E=(E_n)$ is a partition of finite subsets of the positive integers and $pge 1$. 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.https://scma.maragheh.ac.ir/article_18569_d37578addf12775560a0dd1348a14dea.pdf