Some New Cauchy Sequence Spaces

Abstract

In this paper, our goal is to introduce some new Cauchy sequence spaces. These spaces are defined by Cauchy transforms. We shall use notations $C_{\infty }\left( s,t\right) $, $C\left( s,t\right) $ and $C_{0}\left( s,t\right) ~$for these new sequence spaces. We prove that these new sequence spaces $C_{\infty }\left( s,t\right) $, $C\left( s,t\right) $ and $C_{0}\left( s,t\right) ~$ are the $BK-$spaces and isomorphic to the spaces $l_{\infty }$, $c\ $and $c_{0}$, respectively. Besides the bases of these spaces, $\alpha -$, $\beta -\ $and $\gamma -$ duals of these spaces will be given. Finally, the matrix classes $(C\left( s,t\right) :l_{p})$ and $(C\left( s,t\right) :c)$ have been characterized.

Keywords

• cauchy sequence spaces
• $\alpha -$
• $~\beta -\ $and $% \gamma -$ duals
• schauder basis
• matrix mappings