On the paranormed space $\mathcal{M}_{u}(t)$ of double sequences

Feyzi BaÅŸar; HÃ¼samettin Çapan

doi:10.5269/bspm.v37i3.32008

On the paranormed space $\mathcal{M}_{u}(t)$ of double sequences

Authors

Feyzi BaÅŸar Fatih University http://orcid.org/0000-0002-9949-1481
HÃ¼samettin Çapan Istanbul University BeyazÄ±t Campus Graduate School of Natural and Applied Sciences

DOI:

https://doi.org/10.5269/bspm.v37i3.32008

Keywords:

Paranormed double sequence space, Dual spaces, matrix transformations

Abstract

In this paper, we introduce the paranormed sequence space $\mathcal{M}_{u}(t)$ corresponding to the normed space $\mathcal{M}_{u}$ of bounded double sequences. We examine general topological properties of this space and determine its alpha-, beta- and gamma-duals. Furthermore, we characterize some classes of four-dimensional matrix transformations concerning this space and its dual spaces.