Notion of non-absolute family of spaces

Albaidani, Mashael M.; Srivastava, Hari  M.; Ganie, Abdul Hamid

doi:10.22075/ijnaa.2021.24072.2664

Notion of non-absolute family of spaces

Document Type : Research Paper

Authors

Mashael M. Albaidani ¹

Hari M. Srivastava ²^{, 3}

Abdul Hamid Ganie ⁴

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

10.22075/ijnaa.2021.24072.2664

Abstract

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.

Keywords

Sequence spaces

Kothe-duals

Infinite matrix