ON THE PARANORMED TAYLOR SEQUENCE SPACES

Authors : HACER BILGIN ELLIDOKUZOGLU, SERKAN DEMIRIZ

Pages : 132-148

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Publication Date : 2016-10-01

Article Type : Research Paper

Abstract :In this paper, the sequence spaces $t^r_0insert ignore into journalissuearticles values(p);$, $t^r_cinsert ignore into journalissuearticles values(p);$ and $t^rinsert ignore into journalissuearticles values(p);$ of non-absolute type which are the generalization of the Maddox \ sequence spaces have \ been introduced and it is proved that the spaces $t^r_0insert ignore into journalissuearticles values(p);$, $t^r_cinsert ignore into journalissuearticles values(p);$ and $t^rinsert ignore into journalissuearticles values(p);$ are linearly isomorphic to spaces $c_0insert ignore into journalissuearticles values(p);$, $cinsert ignore into journalissuearticles values(p);$ and $\ellinsert ignore into journalissuearticles values(p);$, respectively. Furthermore, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $t^r_0insert ignore into journalissuearticles values(p);$, $t^r_cinsert ignore into journalissuearticles values(p);$ and $t^rinsert ignore into journalissuearticles values(p);$ have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the \ class of matrices $insert ignore into journalissuearticles values(t^r_0insert ignore into journalissuearticles values(p); : \mu);$ has 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 : Taylor sequence spaces, matrix domain, matrix transformations