Notion of non-absolute family of spaces

Document Type : Research Paper


1 Department of Mathematics, College of Science and Humanities Studies, Prince Sattam Bin Abdulaziz University, Al Kharj 11942, Saudi Arabia

2 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada

3 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, Republic of China

4 SSM College of Engineering, Parihaspora, Pattan, Jammu and Kashmir 193121, India


The scenario of this article is to introduce the space $\mathfrak{R}^{t}_s(p, \Delta)$  based on a general Riesz sequence space. Its completeness property is derived and its linear isomorphism property with $\ell(p)$ is proved. The K\"{o}the-dual property of the space $\mathfrak{R}^{t}_s(p, \Delta)$ is also derived. Furthermore, its basis is constructed and some characterization of infinite matrices are given.


Volume 14, Issue 1
January 2023
Pages 345-354
  • Receive Date: 26 July 2021
  • Revise Date: 06 December 2021
  • Accept Date: 16 December 2021