TY - JOUR
ID - 18569
TI - A new sequence space and norm of certain matrix operators on this space
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Roopaei, Hadi
AU - Foroutannia, Davoud
AD - Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.
AD - Department of Mathematics, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran.
Y1 - 2016
PY - 2016
VL - 03
IS - 1
SP - 1
EP - 12
KW - Difference sequence space
KW - Matrix domains
KW - norm
KW - Copson matrix
KW - Hilbert matrix
DO -
N2 - 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_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.
UR - https://scma.maragheh.ac.ir/article_18569.html
L1 - https://scma.maragheh.ac.ir/article_18569_d37578addf12775560a0dd1348a14dea.pdf
ER -