ON THE PARANORMED TAYLOR SEQUENCE SPACES

Abstract

In this paper, the sequence spaces $t^r_0(p)$, $t^r_c(p)$ and $t^r(p)$ of non-absolute type which are the generalization of the Maddox \ sequence spaces have \ been introduced and it is proved that the spaces $t^r_0(p)$, $t^r_c(p)$ and $t^r(p)$ are linearly isomorphic to spaces $c_0(p)$, $c(p)$ and $\ell(p)$, respectively. Furthermore, the $\alpha-,\beta-$ and $\gamma-$duals of the spaces $t^r_0(p)$, $t^r_c(p)$ and $t^r(p)$ 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 $(t^r_0(p) : \mu)$ 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

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