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Zbl 1224.46009
Karakaya, Vatan; Polat, Harun
Some new paranormed sequence spaces defined by Euler and difference operators. (English)
[J] Acta Sci. Math. 76, No. 1-2, 87-100 (2010). ISSN 0001-6969

A linear topological space $X$ over the real field $\Bbb R$ is said to be a paranormed space if there is a subadditive function $h: X\to \Bbb R$ such that $h(\theta)=0$, $h(x)=h(-x)$ and the scalar multiplication is continuous, where $\theta$ denotes the zero vector in $X$. \par In the paper under review, the authors introduce some new paranormed sequence spaces defined by Euler and difference operators (i.e., the sequence spaces $e_0^r(\Delta,p)$, $e_c^r(\Delta,p)$, $e^r_\infty(\Delta,p)$ with $p=(p_k)_{k\in\Bbb N}$ a bounded sequence of positive real numbers) and study some properties of these spaces. In particular, the authors give an inclusion relation between these sequence spaces and study their topological structure. Also, the basis and the $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces are given.
[Angela Albanese (Lecce)]

MSC 2000:: *46A45 Sequence spaces
46B45 Banach sequence spaces

Keywords: paranormed sequence space; matrix mapping; Köthe-Toeplitz duals; Euler and difference sequence spaces

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