On the Paranormed Space L(t) of Double Sequences

Abstract

In this paper, we introduce the paranormed sequence space $\mathcal{L}(t)$ which is the generalization of the space $\mathcal{L}_{q}$ of all absolutely $q-$summable double sequences. We examine some topological properties of the space $\mathcal{L}(t)$ and determine its alpha-, beta- and gamma-duals. Finally, we characterize some classes of four-dimensional matrix transformations from the space $\mathcal{L}(t)$ into some spaces of double sequences.