Some new Pascal sequence spaces

Abstract

The main purpose of the present paper is to study of some new Pascal sequence spaces $p_{\infty }$, $p_{c}$ and $p_{0}$. New Pascal sequence spaces $p_{\infty }$, $p_{c}$ and $p_{0}$ are found as $BK$-spaces and it is proved that the spaces $% p_{\infty }$, $p_{c}$ and $p_{0}~$are linearly isomorphic to the spaces $% l_{\infty }$, $c\ $and $c_{0}$ respectively. Afterward, $\alpha $-, $\beta $% -~and $\gamma $-duals of these spaces $p_{c}$ and $p_{0}$ are computed and their bases are consructed. Finally, matrix the classes $(p_{c}:l_{p})$ and $% (p_{c}:c)$ have been characterized.