Notion of non-absolute family of spaces

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