Roopaei, H., Foroutannia, D. (2016). A new sequence space and norm of certain matrix operators on this space. Sahand Communications in Mathematical Analysis, 3(1), 1-12.

Hadi Roopaei; Davoud Foroutannia. "A new sequence space and norm of certain matrix operators on this space". Sahand Communications in Mathematical Analysis, 3, 1, 2016, 1-12.

Roopaei, H., Foroutannia, D. (2016). 'A new sequence space and norm of certain matrix operators on this space', Sahand Communications in Mathematical Analysis, 3(1), pp. 1-12.

Roopaei, H., Foroutannia, D. A new sequence space and norm of certain matrix operators on this space. Sahand Communications in Mathematical Analysis, 2016; 3(1): 1-12.

A new sequence space and norm of certain matrix operators on this space

^{}Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran.

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.

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