On the paranormed binomial sequence spaces

Authors : Hacer Bilgin Ellidokuzoğlu, Serkan Demiriz, Ali Köseoğlu

Pages : 137-147

Doi:10.32323/ujma.395247

View : 15 | Download : 9

Publication Date : 2018-09-30

Article Type : Research Paper

Abstract :In this paper the sequence spaces $b_0^{r,s}insert ignore into journalissuearticles values(p);$, $b_c^{r,s}insert ignore into journalissuearticles values(p);$, $b_{\infty}^{r,s}insert ignore into journalissuearticles values(p);$ and $b^{r,s}insert ignore into journalissuearticles values(p);$ which are the generalization of the classical Maddox`s paranormed sequence spaces have been introduced and proved that the spaces $b_0^{r,s}insert ignore into journalissuearticles values(p);$, $b_c^{r,s}insert ignore into journalissuearticles values(p);$, $b_{\infty}^{r,s}insert ignore into journalissuearticles values(p);$ and $b^{r,s}insert ignore into journalissuearticles values(p);$ are linearly isomorphic to spaces $c_0insert ignore into journalissuearticles values(p);$, $cinsert ignore into journalissuearticles values(p);$, $\ell_{\infty}insert ignore into journalissuearticles values(p);$ and $\ellinsert ignore into journalissuearticles values(p);$, respectively. Besides this, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $b_0^{r,s}insert ignore into journalissuearticles values(p);$, $b_c^{r,s}insert ignore into journalissuearticles values(p);$, and $b^{r,s}insert ignore into journalissuearticles values(p);$ have been computed, their bases have been constructed and some topological properties of these spaces have been studied. Finally, the classes of matrices $insert ignore into journalissuearticles values(b_0^{r,s}insert ignore into journalissuearticles values(p); : \mu);$, $insert ignore into journalissuearticles values(b^{r,s}_cinsert ignore into journalissuearticles values(p);: \mu);$ and $insert ignore into journalissuearticles values(b^{r,s}insert ignore into journalissuearticles values(p);: \mu);$ have been characterized, where $\mu$ is one of the sequence spaces $\ell_\infty,c$ and $c_0$ and derives the other characterizations for the special cases of $\mu$.
Keywords : Binomial sequence spaces, Paranorm, Matrix domain, Matrix transformations