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

Roopaei, Hadi; Foroutannia, Davoud

Document Type : Research Paper

Authors

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.

Keywords

20.1001.1.23225807.2016.03.1.1.4

Main Subjects

Functional Analysis and Operator Theory

References

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Sahand Communications in Mathematical Analysis

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

References

References

Volume 03, Issue 1 - Serial Number 1
February 2016
Pages 1-12

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

References

References

Volume 03, Issue 1 - Serial Number 1February 2016Pages 1-12

Volume 03, Issue 1 - Serial Number 1
February 2016
Pages 1-12